Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum leng...Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.展开更多
In this paper, we characterize some simple Ka-groups only by using the group order and largest element orders, where a simple K4-group is a simple group of order containing exactly four distinct primes.
Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs＇s work, we introduce the definition of Mπ-groups and provide ...Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs＇s work, we introduce the definition of Mπ-groups and provide a characterization of Mπ-groups.展开更多
In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then ...In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then G is isomorphic to M if and only if the set of the orders of the maximal abelian subgoups of G is the same as that of M .展开更多
Theoretical background and an implementation of the p-group generation algorithm by Newman and O’Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant ...Theoretical background and an implementation of the p-group generation algorithm by Newman and O’Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite p-groups.展开更多
The Γα-group inverse and the Γα-sharp ordering in matrix set are introduced. Some characterizations and properties of the Γα-sharp ordering are given. The relations between the Γα-sharp ordering and the Γα-m...The Γα-group inverse and the Γα-sharp ordering in matrix set are introduced. Some characterizations and properties of the Γα-sharp ordering are given. The relations between the Γα-sharp ordering and the Γα-minus ordering are discussed.展开更多
We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Pro...We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Program,Boston, London, Melbourne, 1981) for irreducible operator. We also show that ifT, T1 and T2 are irreducible operators with T T1≌T T2, then T1≌T2. Finally,weshow that K0 (A(D))≌Z, giving a new result on the K0-group of Banach algebras.展开更多
The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K...The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.展开更多
In order to answer a question motivated by constructing substitution boxes in block ciphers we will exhibit an infinite family of full-rank factorizations of elementary 2-groups into two factors having equal sizes.
Let G be a finite group and N(G)be its norm.Then N(G)is a characteristic subgroup of G which normalizes every subgroup of G.In this paper,we will study the structure of G under one of the following conditions:1)norm q...Let G be a finite group and N(G)be its norm.Then N(G)is a characteristic subgroup of G which normalizes every subgroup of G.In this paper,we will study the structure of G under one of the following conditions:1)norm quotient group G/N(G)is cyclic;2)all Sylow subgroups of G/N(G)are cyclic and in particular if the order of G/N(G)is a square-free number.展开更多
This work deals with the power exponent 1rand 2r respectively of the maximal and second-maximal prime factors of the order of simple K4-group, and the classification for simple 4{5,7}K--group G (i.e. G can not be divi...This work deals with the power exponent 1rand 2r respectively of the maximal and second-maximal prime factors of the order of simple K4-group, and the classification for simple 4{5,7}K--group G (i.e. G can not be divided by 5 nor by 7 or ()Gp= 4 ), simple 5 -4K-group G (i.e. G can not divided by 5 and ()Gp=4) and simple 7-4K-group G (i.e. G can not divided by 7 and ()Gp= 4). It is derived that 1r =1, 2 and 4, and 2r is not greater than 4. All the simple 4K-groups with order 235,237abcdabcdpp and 2357abcd are obtained.展开更多
This paper is a survey on the recent work of the authors and their col-laborators on the Classification of Inductive Limit C*-algebras. Some examples are presented to explain several important ideas.
Suppose that G is a finite p-group.If all subgroups of index p^(t)of G are abelian and at least one subgroup of index p^(t−1)of G is not abelian,then G is called an A_(t)-group.We useA0-group to denote an abelian grou...Suppose that G is a finite p-group.If all subgroups of index p^(t)of G are abelian and at least one subgroup of index p^(t−1)of G is not abelian,then G is called an A_(t)-group.We useA0-group to denote an abelian group.From the definition,we know every finite non-abelian p-group can be regarded as an A_(t)-group for some positive integer t.A_(1)-groups and A_(2)-groups have been classified.Classifying A_(3)-groups is an old problem.In this paper,some general properties about A_(t)-groups are given.A_(3)-groups are completely classified up to isomorphism.Moreover,we determine the Frattini subgroup,the derived subgroup and the center of every A_(3)-group,and give the number of A_(1)-subgroups and the triple(μ_(0),μ_(1),μ_(2))of every A_(3)-group,whereμi denotes the number of A_(i)-subgroups of index p of A_(3)-groups.展开更多
This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's suf...This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.展开更多
Let G be a finite p-group.If the order of the derived subgroup of each proper subgroup of G divides pi,G is called a Di-group.In this paper,we give a characterization of all D1-groups.This is an answer to a question i...Let G be a finite p-group.If the order of the derived subgroup of each proper subgroup of G divides pi,G is called a Di-group.In this paper,we give a characterization of all D1-groups.This is an answer to a question introduced by Berkovich.展开更多
Let H olenote a complex separable Hilbert space and L(H)denote the collection of bounded linear operators on H.An operator T∈L(H)is said to be strongly irreducible if T does not commute with any nontrivial idempotent...Let H olenote a complex separable Hilbert space and L(H)denote the collection of bounded linear operators on H.An operator T∈L(H)is said to be strongly irreducible if T does not commute with any nontrivial idempotent.Herrero and Jiang showed that the norm-closure of the class of all strongly irreducible operators is the class of all operators with connected spectrum.This result can be considered as an"approximate inverse"of the Riesz decomposition theorem.In the paper,we give a more precise characterization of approximate invariants of strongly irreducible operators.The main result is:For any T∈L(H)with connected spectrum andε>0,there exists a strongly irreducible operator A,such that A-T<ε,V(A(A))=~N,K0(A(A))~=Z,and A(A)/rad A(A)is commutative,where A(A)denotes the commutant of A and rad A(A)denotes the Jacobson radical of A(A).The research is inspired by the recent similarity classification technique of Cowen-Douglas operators of Jiang Chunlan.展开更多
基金supported by the National Natural Science Foundation of China(No.12301425)。
文摘Let G be a finite abelian group and k be a positive integer.The Davenport constant is a central invariant in zero-sum thoery.The invariant Dk(G)generalizes the Davenport constant D(G)and is defined as the maximum length l such that there exists a sequenceB of length l overGcontaining k disjoint non-empty zero-sum subsequences.This paper studies the inverse problem associated with this invariant for the elementary abelian 2-groups C_(2)^(r).For r∈[2,4],we characterize the structures of zero-sum sequences of length D2(C_(2)^(r))and D2(C_(2)^(r))-1 in C_(2)^(r) that can be decomposed into at most two minimal zero-sum subsequences.For r∈[2,5],we characterize the structures of sequences of length D2(C_(2)^(r))-1.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1117136411271301)+2 种基金the Natural Science Foundation Project of CQ CSTC(Grant No.2014jcyjA00004)the Science and Technology Project of Chongqing Education Committee(Grant No.KJ1400520)the Foundation Project of Chongqing Normal University(Grant No.14XYY026)
文摘In this paper, we characterize some simple Ka-groups only by using the group order and largest element orders, where a simple K4-group is a simple group of order containing exactly four distinct primes.
基金Supported by NSF of China(1117116911071155)the B.S.Foundation of Shandong Province(BS2012SF003)
文摘Let π be a set of primes. Isaacs established the π-theory of characters, which generalizes the theory of Brauer modular characters. Motivated by Isaacs＇s work, we introduce the definition of Mπ-groups and provide a characterization of Mπ-groups.
文摘In this paper, We show that the simple K\-3-groups can be characterized by the orders of their maximal abelian subgroups. That is, we have Theorem Let G be a finite group and M a simple K \-3-group. Then G is isomorphic to M if and only if the set of the orders of the maximal abelian subgoups of G is the same as that of M .
文摘Theoretical background and an implementation of the p-group generation algorithm by Newman and O’Brien are used to provide computational evidence of a new type of periodically repeating patterns in pruned descendant trees of finite p-groups.
基金the National Sciennce Foundation of Zhejiang Province(Y604089)
文摘The Γα-group inverse and the Γα-sharp ordering in matrix set are introduced. Some characterizations and properties of the Γα-sharp ordering are given. The relations between the Γα-sharp ordering and the Γα-minus ordering are discussed.
基金The 973 Project of China and the NNSF (Grant No. 19631070) of China.
文摘We show that two irreducible operators on H are unitari1y equivalentif and only if W*(A B)’≌M2(C), and give an answer to the open question posedby J. B. Conway (Subnormal Operators, πPitman, Advanced Publishing Program,Boston, London, Melbourne, 1981) for irreducible operator. We also show that ifT, T1 and T2 are irreducible operators with T T1≌T T2, then T1≌T2. Finally,weshow that K0 (A(D))≌Z, giving a new result on the K0-group of Banach algebras.
文摘The present note determines the structure of the K2-group and of its subgroup over a finite commutative ring R by considering relations between R andfinite commutative local ring Ri (1 < i < m), where R Ri and K2(R) =K2(Ri). We show that if charKi= p (Ki denotes the residual field of Ri), then K2(Ri) and its subgroups must be p-groups.
文摘In order to answer a question motivated by constructing substitution boxes in block ciphers we will exhibit an infinite family of full-rank factorizations of elementary 2-groups into two factors having equal sizes.
基金Supported by the National Natural Science Foundation of China(Grant No.11661023)the Service Industry Development Guide of Guizhou Province(Grant No.Qian Fa Gai Fu Wu[2018]1181)。
文摘Let G be a finite group and N(G)be its norm.Then N(G)is a characteristic subgroup of G which normalizes every subgroup of G.In this paper,we will study the structure of G under one of the following conditions:1)norm quotient group G/N(G)is cyclic;2)all Sylow subgroups of G/N(G)are cyclic and in particular if the order of G/N(G)is a square-free number.
文摘This work deals with the power exponent 1rand 2r respectively of the maximal and second-maximal prime factors of the order of simple K4-group, and the classification for simple 4{5,7}K--group G (i.e. G can not be divided by 5 nor by 7 or ()Gp= 4 ), simple 5 -4K-group G (i.e. G can not divided by 5 and ()Gp=4) and simple 7-4K-group G (i.e. G can not divided by 7 and ()Gp= 4). It is derived that 1r =1, 2 and 4, and 2r is not greater than 4. All the simple 4K-groups with order 235,237abcdabcdpp and 2357abcd are obtained.
基金Both authors are supported by NSF grant DMS9970840 This material is also based uponwork supported by,the U.S. Army Research Office under grant number DAADl9-00-1-0152 for both authors.
文摘This paper is a survey on the recent work of the authors and their col-laborators on the Classification of Inductive Limit C*-algebras. Some examples are presented to explain several important ideas.
基金This work was supported by NSFC(Nos.11371232,11471198)by NSF of Shanxi Province(No.2013011001).
文摘Suppose that G is a finite p-group.If all subgroups of index p^(t)of G are abelian and at least one subgroup of index p^(t−1)of G is not abelian,then G is called an A_(t)-group.We useA0-group to denote an abelian group.From the definition,we know every finite non-abelian p-group can be regarded as an A_(t)-group for some positive integer t.A_(1)-groups and A_(2)-groups have been classified.Classifying A_(3)-groups is an old problem.In this paper,some general properties about A_(t)-groups are given.A_(3)-groups are completely classified up to isomorphism.Moreover,we determine the Frattini subgroup,the derived subgroup and the center of every A_(3)-group,and give the number of A_(1)-subgroups and the triple(μ_(0),μ_(1),μ_(2))of every A_(3)-group,whereμi denotes the number of A_(i)-subgroups of index p of A_(3)-groups.
基金supported by the National Natural Science Foundation of China(Grant No.10471025)the Natural Science Foundation of Fujian Province of China(Grant Nos.F0210014&Z0511019).
文摘This paper merges some classifications of G-M-type Banach spaces simplifically, discusses the condition of K0(B(X)) = 0 for operator algebra B(X) on a Banach space X, and obtains a result to improve Laustsen's sufficient condition, gives an example to show that X ≈ X2 is not a sufficient condition of K0(B(X)) = 0.
基金supported by National Natural Science Foundation of China (Grant Nos.10571128,10871032)Natural Science Foundation of Jiangsu Province (Grant No.BK2008156)Suzhou City Senior Talent Supporting Project
文摘Let G be a finite p-group.If the order of the derived subgroup of each proper subgroup of G divides pi,G is called a Di-group.In this paper,we give a characterization of all D1-groups.This is an answer to a question introduced by Berkovich.
基金supported by the National Natural Science Foundation of China(Grant No.10571041)Hebei Provincial Natural Science Foundation(Grant No.A2005000006)
文摘Let H olenote a complex separable Hilbert space and L(H)denote the collection of bounded linear operators on H.An operator T∈L(H)is said to be strongly irreducible if T does not commute with any nontrivial idempotent.Herrero and Jiang showed that the norm-closure of the class of all strongly irreducible operators is the class of all operators with connected spectrum.This result can be considered as an"approximate inverse"of the Riesz decomposition theorem.In the paper,we give a more precise characterization of approximate invariants of strongly irreducible operators.The main result is:For any T∈L(H)with connected spectrum andε>0,there exists a strongly irreducible operator A,such that A-T<ε,V(A(A))=~N,K0(A(A))~=Z,and A(A)/rad A(A)is commutative,where A(A)denotes the commutant of A and rad A(A)denotes the Jacobson radical of A(A).The research is inspired by the recent similarity classification technique of Cowen-Douglas operators of Jiang Chunlan.
