A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups....A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups. Two sufficient and necessary conditions for such graphs to be 1- or 2-arcregular are given and based on the conditions, several infinite families of 1- or 2-arc-regular cubic Cayley graphs of alternating groups are constructed.展开更多
Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p^3. Let P1-groups denote the p-groups all of whose minimal nonabelian subgroups are nonme tacyclic of or...Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p^3. Let P1-groups denote the p-groups all of whose minimal nonabelian subgroups are nonme tacyclic of order p^3. In this paper, the P1-groups are classified, and as a by-product, we prove the Hughes' conjecture is true for the P1-groups.展开更多
In this paper,we study the structure of nonabelian omni-Lie algebroids.Firstly,taking Lie algebroid(E,[·,·]_(E,ρE))as the starting point,a nonabelian omni-Lie algebroid is defined on direct sum bundle DE⊕J...In this paper,we study the structure of nonabelian omni-Lie algebroids.Firstly,taking Lie algebroid(E,[·,·]_(E,ρE))as the starting point,a nonabelian omni-Lie algebroid is defined on direct sum bundle DE⊕JE,where DE and JE are,respectively,the gauge Lie algebroid and the jet bundle of vector bundle E,and study its properties.Furthermore,it is concluded that the nonabelian omni-Lie algebroid is a trivial deformation of the omni-Lie algebroid,and the nonabelian omni-Lie algebroid is a matched pair of Leibniz algebroids.展开更多
A finite group G is said to be a Bn-group if any n-element subset A={a1,a2,...,an}of G satisfies∣∣A^2∣∣=|{aiaj|1≤i,j≤n}|≤n(n+1)/2.In this paper,the characterizations of the B6-and B7-groups are given.
For an odd prime p,we give a criterion for finite p-groups whose nonnormal subgroups are metacyclic,and based on the criterion,the p-groups whose nonnormal subgroups are metacyclic are classified up to isomorphism.Thi...For an odd prime p,we give a criterion for finite p-groups whose nonnormal subgroups are metacyclic,and based on the criterion,the p-groups whose nonnormal subgroups are metacyclic are classified up to isomorphism.This solves a problem proposed by Berkovich.展开更多
Assume G is a group of order 2^(n),n≥5.Let s_(k)(G)denote the number of subgroups of order 2^(k) of G.We classify finite 2-groups G with s k(G)≤2^(4),where 1≤k≤n.
In this paper we investigate the title groups which we call isomaximal. We give the list of all isomaximal 2-groups with abelian maximal subgroups. Further, we prove some properties of isomaximal 2-groups with nonabel...In this paper we investigate the title groups which we call isomaximal. We give the list of all isomaximal 2-groups with abelian maximal subgroups. Further, we prove some properties of isomaximal 2-groups with nonabelian maximal subgroups. After that, we investigate the structure of isomaximal groups of order less than 64. Finally, in Theorem 14. we show that the minimal nonmetacyclic group of order 32 possesses a unique isomaximal extension of order 64.展开更多
Let G be a finite nonabelian group which has no abelian maximal subgroups and satisfies that any two non-commutative elements generate a maximal subgroup. Then G is isomorphic to the smallest Suzuki 2-group of order 64.
基金supported by Guangxi Science Foundations (Grant No. 0832054)Guangxi Postgraduate Education Innovation Research (Grant No. 2008105930701M102)
文摘A graph is said to be s-arc-regular if its full automorphism group acts regularly on the set of its s-arcs. In this paper, we investigate connected cubic s-arc-regular Cayley graphs of finite nonabelian simple groups. Two sufficient and necessary conditions for such graphs to be 1- or 2-arcregular are given and based on the conditions, several infinite families of 1- or 2-arc-regular cubic Cayley graphs of alternating groups are constructed.
基金Supported by National Natural Science Foundation of China(Grant Nos.11771258 and 11471198)
文摘Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p^3. Let P1-groups denote the p-groups all of whose minimal nonabelian subgroups are nonme tacyclic of order p^3. In this paper, the P1-groups are classified, and as a by-product, we prove the Hughes' conjecture is true for the P1-groups.
基金supported by the National Natural Science Foundation of China(Grant Nos.11961049,11601219).
文摘In this paper,we study the structure of nonabelian omni-Lie algebroids.Firstly,taking Lie algebroid(E,[·,·]_(E,ρE))as the starting point,a nonabelian omni-Lie algebroid is defined on direct sum bundle DE⊕JE,where DE and JE are,respectively,the gauge Lie algebroid and the jet bundle of vector bundle E,and study its properties.Furthermore,it is concluded that the nonabelian omni-Lie algebroid is a trivial deformation of the omni-Lie algebroid,and the nonabelian omni-Lie algebroid is a matched pair of Leibniz algebroids.
基金The second author acknowledges the support of the Jiangsu University(Grant No.5501190011).
文摘A finite group G is said to be a Bn-group if any n-element subset A={a1,a2,...,an}of G satisfies∣∣A^2∣∣=|{aiaj|1≤i,j≤n}|≤n(n+1)/2.In this paper,the characterizations of the B6-and B7-groups are given.
基金supported by National Natural Science Foundation of China(Grant Nos.11771258 and 11471198)。
文摘For an odd prime p,we give a criterion for finite p-groups whose nonnormal subgroups are metacyclic,and based on the criterion,the p-groups whose nonnormal subgroups are metacyclic are classified up to isomorphism.This solves a problem proposed by Berkovich.
基金supported by the National Natural Science Foundation of China(Nos.11371232,11101252)the Shanxi Provincial Natural Science Foundation of China(No.2013011001)the Fundamental Research Funds for the Central Universities(No.BUPT2013RC0901)
文摘The groups as mentioned in the title are classified up to isomorphism. This is an answer to a question proposed by Berkovich and Janko.
文摘Assume G is a group of order 2^(n),n≥5.Let s_(k)(G)denote the number of subgroups of order 2^(k) of G.We classify finite 2-groups G with s k(G)≤2^(4),where 1≤k≤n.
基金supported by Ministry of Science, Education and Sports of Republic of Croatia (Grant No.036-0000000-3223)
文摘In this paper we investigate the title groups which we call isomaximal. We give the list of all isomaximal 2-groups with abelian maximal subgroups. Further, we prove some properties of isomaximal 2-groups with nonabelian maximal subgroups. After that, we investigate the structure of isomaximal groups of order less than 64. Finally, in Theorem 14. we show that the minimal nonmetacyclic group of order 32 possesses a unique isomaximal extension of order 64.
基金NSFC (No.10671114)NSF of Shanxi Province (No.20051007)the Returned Overseas(student) Fund of Shanxi province (No.[2007]13-56)
文摘Let G be a finite nonabelian group which has no abelian maximal subgroups and satisfies that any two non-commutative elements generate a maximal subgroup. Then G is isomorphic to the smallest Suzuki 2-group of order 64.
