Recall that a subgroup H of a finite group G is called a TI-subgroup if H ∩ H^9 = 1 or H for each g ∈ G. Suppose that G is a finite group whose second maximal subgroups are TI-subgroups. It is shown that every class...Recall that a subgroup H of a finite group G is called a TI-subgroup if H ∩ H^9 = 1 or H for each g ∈ G. Suppose that G is a finite group whose second maximal subgroups are TI-subgroups. It is shown that every class-preserving Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result, we obtain that the normalizer property holds for G.展开更多
In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Fi...In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.展开更多
In this paper, we determine the order of automorphism group of p-groups in the third family ( Φ 3) and the fourth family ( Φ 4) in [1], whose order is p^6(p≥3). Here p denotes an odd prime.
In the paper we obtain two infinite classes of p-groups, calculate the orders of their automorphism groups and correct a mistake（perhaps misprinted） of Rodney James＇ paper in 1980.
Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1,...Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1, i}. This paper proves that f: T*n(F) → T*n(F) is a group automorphism if and only if there exist a matrix Q in T*n(F) and a field automorphism rs of F such that either where A = ((aij)), A-T is the transpose inverse of A, J = Ei n+1-i, and : i= 1T*n(F) → F* is a homomorphism which satisfies {(xIn)(x)x F*} = F* and {x F*(xIn)(x) = 1} = {1}. Simultaneously, they also determine the automorphisms of STn(F).展开更多
Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）,...Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.展开更多
Let G be a primitive group. It is proved that there exits some prime p such that every p-central automorphism of G is inner. As an application, it is proved that every Coleman automorphism of the holomorph of G is inn...Let G be a primitive group. It is proved that there exits some prime p such that every p-central automorphism of G is inner. As an application, it is proved that every Coleman automorphism of the holomorph of G is inner. In particular, the normalizer property holds for such groups in question. Additionally, other related results are obtained as well.展开更多
We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtain...We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.展开更多
In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism group...In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism groups of all p-groups of orders less than p6 under the P Hall's concept of isoclinism,also make a number of corrections for orders of automorphism groups offered for a mistake or fault before.展开更多
In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T（D（VN,F））,which acting on the normal Siegel domain D（VN,F）is simple and transitive,and prove that the max...In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T（D（VN,F））,which acting on the normal Siegel domain D（VN,F）is simple and transitive,and prove that the maximal connected automorphism group of T（D（VN,F））is its maximal connected inner automorphism group.展开更多
Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney Ja...Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.展开更多
In this paper, the automorphism group is completely determined, of the unitary Cayley graph, the unit graph and the total graph, over the ring of Gaussian integers modulo a prime power.
Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to...Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.展开更多
We know that for a code C,it‘s very important to find out the Automorphism groupAutC of C.However,it is very difficult to seek entire AutC.In this paper,using the G.I of matrices over a finite field,we give several m...We know that for a code C,it‘s very important to find out the Automorphism groupAutC of C.However,it is very difficult to seek entire AutC.In this paper,using the G.I of matrices over a finite field,we give several methods to judge whether a permutation σ∈S_n.(Symmetric group) belongs to AutC or not.They are helpful for the purpose to ex-展开更多
Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant...Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant under the admissible groups relative to Lie algebras of Cartan type X.展开更多
Let G be a finite group and Outcoz（G） the Coleman outer automorphism group of G（for the definition, see below）. The question whether Outcol（G） is a p′-group naturally arises from the study of the normalizer pro...Let G be a finite group and Outcoz（G） the Coleman outer automorphism group of G（for the definition, see below）. The question whether Outcol（G） is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol（G） to be a p＇-group are obtained. Our results generalize some well-known theorems.展开更多
Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-alge...Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）.展开更多
Let R be a prime ring, L a noncentral Lie ideal and a nontrivialautomorphism of R such that us（u）ut = 0 for all u 2 L, where s; t are fixednon-negative integers. If either charR 〉 s ＋ t or charR = 0, then R satis...Let R be a prime ring, L a noncentral Lie ideal and a nontrivialautomorphism of R such that us（u）ut = 0 for all u 2 L, where s; t are fixednon-negative integers. If either charR 〉 s ＋ t or charR = 0, then R satisfies s4, thestandard identity in four variables. We also examine the identity （σ（[x; y]）-[x; y]）n =0 for all x; y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. Ifeither charR 〉 n or charR = 0, then R is commutative.展开更多
Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomp...Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117116911071155)the Doc-toral Foundation of Shandong Province(Grant No.BS2012SF003)
文摘Recall that a subgroup H of a finite group G is called a TI-subgroup if H ∩ H^9 = 1 or H for each g ∈ G. Suppose that G is a finite group whose second maximal subgroups are TI-subgroups. It is shown that every class-preserving Coleman automorphism of G is an inner automorphism. As an immediate consequence of this result, we obtain that the normalizer property holds for G.
文摘In this paper, we define the concept of (right) partial generalized automorphisms and discuss the extension problem, and also give a characterization of (right) partial generalized automorphisms of semiprime rings. Finally, we study the centralizing problem of right partial generalized automorphisms.
文摘In this paper, we determine the order of automorphism group of p-groups in the third family ( Φ 3) and the fourth family ( Φ 4) in [1], whose order is p^6(p≥3). Here p denotes an odd prime.
基金Supported by NNSF of China(60574052)Supported by NSF(05001820)Supported by PST of Guangdong(2005B33301008)
文摘In the paper we obtain two infinite classes of p-groups, calculate the orders of their automorphism groups and correct a mistake（perhaps misprinted） of Rodney James＇ paper in 1980.
基金This work is supported by NSF of China NSF of Heilongjiang province
文摘Suppose F is a field of characteristic not 2 and F* its multiplicative group. Let T*n(F) be the multiplicative group of invertible upper triangular n x n matrices over F and STn(F) its subgroup {(aij) E T*n(F)aii = 1, i}. This paper proves that f: T*n(F) → T*n(F) is a group automorphism if and only if there exist a matrix Q in T*n(F) and a field automorphism rs of F such that either where A = ((aij)), A-T is the transpose inverse of A, J = Ei n+1-i, and : i= 1T*n(F) → F* is a homomorphism which satisfies {(xIn)(x)x F*} = F* and {x F*(xIn)(x) = 1} = {1}. Simultaneously, they also determine the automorphisms of STn(F).
基金The NSF(11371124)of Chinathe NSF(F2015402033)of Hebei Provincethe Doctoral Special Foundation(20120066)of Hebei University of Engineering
文摘Let G be a finitely generated torsion-free nilpotent group and a an automorphism of prime order p of G. If the map ψ ： G → G defined by g^φ = [g, α] is surjective, then the nilpotent class of G is at most h（p）, where h（p） is a function depending only on p. In particular, if α^3 = 1, then the nilpotent class of G is at most 2.
基金Supported by the National Natural Science Foundation of China(Grant No.71571108)Projects of International(Regional)Cooperation and Exchanges of NSFC(Grant Nos.71611530712+4 种基金 61661136002)Specialized Research Fund for the Doctoral Program of Higher Education of China(Grant No.20133706110002)Natural Science Foundation of Shandong Province(Grant No.ZR2015GZ007)Project Funded by China Postdoctoral Science Foundation(Grant No.2016M590613)the Specialized Fund for the Postdoctoral Innovative Research Program of Shandong Province(Grant No.201602035)
文摘Let G be a primitive group. It is proved that there exits some prime p such that every p-central automorphism of G is inner. As an application, it is proved that every Coleman automorphism of the holomorph of G is inner. In particular, the normalizer property holds for such groups in question. Additionally, other related results are obtained as well.
基金Supported by the PCI of the UCA ‘Teoría de Lie y Teoría de Espacios de Banachthe PAI with project numbers FQM-298 and FQM-336the project of the Spanish Ministerio de Educación y Ciencia MTM2004-06580-C02-02 and with fondos FEDER
文摘We study the Banach-Lie group Ltaut（A） of Lie triple automorphisms of a complex associative H^＊-algebra A. Some consequences about its Lie algebra, the algebra of Lie triple derivations of A, Ltder（A）, are obtained. For a topologically simple A, in the infinite-dimensional case we have Ltaut（A）0 = Aut（A） implying Ltder（A） = Der（A）. In the finite-dimensional case Ltaut（A）0 is a direct product of Aut（A） and a certain subgroup of Lie derivations δ from A to its center, annihilating commutators.
基金Supported by the National Natural Science Foundation of China(61074185)Supported by the Projection of Science and Technique for Guangdong Province(2009B030802044)+1 种基金Supported by the Projection of Production,Study and Investigation for Guangdong Province(2010B090301042)Supported by the Science and Study Foundation of Guangxi University(XB2100285)
文摘In this paper by techniques of group we give some formulae for solving the general quadratic equations of two variables over a finite field,completely calculate and uniformly deal with the orders of automorphism groups of all p-groups of orders less than p6 under the P Hall's concept of isoclinism,also make a number of corrections for orders of automorphism groups offered for a mistake or fault before.
基金Supported by the National Science Foundation of China（11047030） Supported by the Natural Science Foundation of Henan Provincial Education Department（2010B11003） Supported by the Natural Science Foundation of Henan University（2009YBZR025）
文摘In this paper,the authors determine maximal connected automorphism group of the Lie transformation group T（D（VN,F））,which acting on the normal Siegel domain D（VN,F）is simple and transitive,and prove that the maximal connected automorphism group of T（D（VN,F））is its maximal connected inner automorphism group.
基金The Science Research Foundation of Chongqing Municipal Education Commission of China(KJ050611)
文摘Using the metabelian property, regularity, p-commutativity and some properties of congruence, this paper gave the orders of automorphism groups of family Ф24, which are the groups of order p^6 determined by Rodney James, where p denotes an odd prime.
基金Supported by the National Natural Science Foundation of China(Grant No.11771176)。
文摘In this paper, the automorphism group is completely determined, of the unitary Cayley graph, the unit graph and the total graph, over the ring of Gaussian integers modulo a prime power.
基金Supported by the Fundamental Research Funds for the Central Universities
文摘Let F be a field of characteristic not 2, and let A be a finite-dimensional semisimple F -algebra. All local automorphisms of A are characterized when all the degrees of A are larger than 1. If F is further assumed to be an algebraically closed field of characteristic zero, K a finite group, F K the group algebra of K over F , then all local automorphisms of F K are also characterized.
文摘We know that for a code C,it‘s very important to find out the Automorphism groupAutC of C.However,it is very difficult to seek entire AutC.In this paper,using the G.I of matrices over a finite field,we give several methods to judge whether a permutation σ∈S_n.(Symmetric group) belongs to AutC or not.They are helpful for the purpose to ex-
基金The NSF(11171055)of Chinathe NSF(JC201004 and A200903)of Heilongjiang Province of Chinathe NSF(12511349)of Heilongjiang Educational Committee of China
文摘Let X denote a finite or infinite dimensional Lie algebra of Cartan type W, S, H or K over a field of characteristic p 〉 3. In this paper it is proved that certain filtrations of the underlying algebras are invariant under the admissible groups relative to Lie algebras of Cartan type X.
基金Supported by NSF of China(11171169)the B.S.Foundation of Shandong Province(BS2012SF003)
文摘Let G be a finite group and Outcoz（G） the Coleman outer automorphism group of G（for the definition, see below）. The question whether Outcol（G） is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol（G） to be a p＇-group are obtained. Our results generalize some well-known theorems.
文摘Let Tn＋1 （R） be upper matrix algebra of order n ＋ 1 over a 2-torsion free commutative ring R with identity. In this paper, we find an automorphism, which is fixed by all orthogonal idempotents and is not an R-algebra aulomorphism, of Tn＋1 （R）. Furthermore we prove that this aulomorphism is an involutive Jordan automorphism of Tn＋1 （R）.
基金The NSF(1408085QA08) of Anhui Provincethe Natural Science Research Foundation(KJ2014A183) of Anhui Provincial Education DepartmentAnhui Province College Excellent Young Talents Fund Project(2012SQRL155) of China
文摘Let R be a prime ring, L a noncentral Lie ideal and a nontrivialautomorphism of R such that us（u）ut = 0 for all u 2 L, where s; t are fixednon-negative integers. If either charR 〉 s ＋ t or charR = 0, then R satisfies s4, thestandard identity in four variables. We also examine the identity （σ（[x; y]）-[x; y]）n =0 for all x; y ∈ I, where I is a nonzero ideal of R and n is a fixed positive integer. Ifeither charR 〉 n or charR = 0, then R is commutative.
文摘Let T(R) be a two-order upper matrix algebra over the semilocal ring R which is determined by R=F×F where F is a field such that CharF=0. In this paper, we prove that any Jordan automorphism of T(R) can be decomposed into a product of involutive, inner and diagonal automorphisms.
