A subgroup H of a finite group G is called a TI-subgroup if H ∩ H^x = 1 or H for all x ∈ G. In this paper, a complete classification for finite p-groups, in which all abelian subgroups are TI-subgroups, is given.
In this paper, a finite group G with IAut（G） ： P（G）I ^- p or pq is determined, where P（G） is the power automorphism group of G, and p, q are distinct primes. Especially, we prove that a finite group G satisfies...In this paper, a finite group G with IAut（G） ： P（G）I ^- p or pq is determined, where P（G） is the power automorphism group of G, and p, q are distinct primes. Especially, we prove that a finite group G satisfies ｜Aut（G） ： P（G）｜= pq if and only if Aut（G）/P（G） ≌S3. Also, some other classes of finite groups are investigated and classified, which are necessary for the proof of our main results.展开更多
In this paper the classification is given for finite groups in which the normalizer of every non-normal cyclic subgroup of order divided by the minimal prime of |G| is a maximal subgroup.
In this paper, the so-called π-cover-avoiding properties of subgroups are defined and investigated. In terms of this property, we characterize the π-solvability of finite groups. Some other new results are also obta...In this paper, the so-called π-cover-avoiding properties of subgroups are defined and investigated. In terms of this property, we characterize the π-solvability of finite groups. Some other new results are also obtained based on the assumption that some subgroups have the semi cover-avoiding properties in a finite group.展开更多
基金the Natural Science Foundation of China(10161001)the Natural Science Foundation of Guangxi of China+1 种基金the National Natural Science Foundation of Shanghai Education CommitteeSpecial Funds for Major Specialities of Shanghai Education Committee
文摘A subgroup H of a finite group G is called a TI-subgroup if H ∩ H^x = 1 or H for all x ∈ G. In this paper, a complete classification for finite p-groups, in which all abelian subgroups are TI-subgroups, is given.
基金supported by National Natural Science Foundation of China (Grant No. 10771132)SGRC (Grant No. GZ310)+1 种基金Shanghai Leading Academic Discipline Project (Grant No. J50101)Science Technology Foundation of Shanxi Province for Colleges (Grant No. 20081022)
文摘In this paper, a finite group G with IAut（G） ： P（G）I ^- p or pq is determined, where P（G） is the power automorphism group of G, and p, q are distinct primes. Especially, we prove that a finite group G satisfies ｜Aut（G） ： P（G）｜= pq if and only if Aut（G）/P（G） ≌S3. Also, some other classes of finite groups are investigated and classified, which are necessary for the proof of our main results.
基金Supported by the Doctoral Scientific Research Foundation of Shanxi University of Finance and Economics(Grant No.Z18207)the National Natural Science Foundation of China(Grant Nos.11771271,11801334)the China Scholarship Council Foundation(Grant No.201908140049)。
文摘In this paper the classification is given for finite groups in which the normalizer of every non-normal cyclic subgroup of order divided by the minimal prime of |G| is a maximal subgroup.
基金Supported by the National Natural Science Foundation of China (Grant No. 10771132)the Science and Technology Foundation of Shanxi Province for Colleges (Grant No. 20081022)the Team Innovation Research Foundation of Shanxi University of Finance and Economics
文摘In this paper, the so-called π-cover-avoiding properties of subgroups are defined and investigated. In terms of this property, we characterize the π-solvability of finite groups. Some other new results are also obtained based on the assumption that some subgroups have the semi cover-avoiding properties in a finite group.
