真商群为s-自对偶群的有限p-群

如果有限群G的每个子群与G的某个商群同构,则称群G为s-自对偶群.如果s-自对偶群G的每个商群与G的某个子群同构,则称群G为自对偶群.本文分类了每个真商群均为s-自对偶群的有限p-群.作为推论,本文还分类了每个真截段均为s-自对偶群的有限p-群,每个真商群均为自对偶群的有限p-群,以及每个真截段均为自对偶群的有限p-群...     

可除阿贝尔p-群的自同构群

主要探讨了秩大于或者等于p-1的可除阿贝尔p-群的p-自同构群,并且得到这些p-自同构如何作用在该可除阿贝尔p-群上.这些结论有助于进一步理解Cernikov p-群的结构.     

所有子群皆循环或正规的有限2-群

研究了所有子群皆循环或正规的有限2群,并给出了其完全分类.     

Finite p-groups All of Whose Minimal Nonabelian Subgroups are Nonmetacyclic of Order p3

Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p³. Let P₁-groups denote the p-groups all of whose minimal nonabelian subgroups are nonmetacyclic of order p³. In this paper, the P₁-groups are classified, and as a by-product, we prove the Hughes' conjecture is true for the P₁-groups.     

Finite p-Groups in Which the Number of Subgroups of Possible Order is Less Than or Equal to $p^3 $

In this paper, groups of order pn in which the number of subgroups of possible order is less than or equal to p3 are classified. It turns out that if p 2, n ≥ 5, then the classification of groups of order pn in which the number of subgroups of possible order is less than or equal to p3 and the classification of groups of order pn with a cyclic subgroup of index p2 are the same.     

最大Abel商群为局部循环群的可解群

从自同构群的角度出发,给出了一些具有有限性条件的、最大Abel商群为局部循环群的可解群的结构．     

关于有限Abel p-群的自同构群

从有限Abel p-群P的型不变量出发,给出了其自同构群AutP的阶的计算公式,并利用|AutP|的计算公式得到了下面3个结果:1.由有限Abel p-群的型不变量的两种变换得到了其自同构群的阶的变化规律;2.用群的阶、秩、幂指数三个量界定了有限Abel p-群的自同构的阶;3.对部分Frattini子群为p阶群的有限p-群,确定了其自同构群的阶何时达到最小值和最大值.     

内交换p群的中心扩张(Ⅱ)

设N,H是任意的群.若存在群G,它具有正规子群N≤Z(G),使得N≌N且G/N≌H,则称群G为N被H的中心扩张.本文完全分类了当N为循环p群,H为内交换p群时,N被H的中心扩张得到的所有不同构的群.     

On Finite p-Groups Whose IA-Automorphisms Are All Class Preserving

Let G be a finite non-abelian p-group, where p is a prime. An automorphism α of G is called a class preserving automorphism if α(x) ∈ x ^G the conjugacy class of x in G, for all x ∈ G. An automorphism α of G is called an IA-automorphism if x ^?1α(x) ∈ G′ for each x ∈ G. In this paper, we give necessary and sufficient conditions on finite p-group G of nilpotency class 2 such that every IA-automorphism is class preserving.     

交换子群较小的一类有限p群

研究了阶为p(m(m+1)/2)且交换子群的最大阶为p(m)的有限群,得到了这类特殊的p群的几个性质,给出了满足极大类条件的这类p群的同构分类.     

Finite p-Groups All of Whose Minimal Nonnormal Subgroups Posses Large Normal Closures

We obtained some results about finite p-groups G with G/H^G being abelian for all nonnormal subgroups H, where H^G denotes the normal closure of H. Moreover, we give a classification of finite p-groups G with G/H^G being cyclic for all nonnormal subgroups H.     

Finite Exceptional p-Groups of Small Order

A finite group is said to be exceptional if its minimal degree of a faithful permutation representation is strictly less than that of one of its factor groups, called a distinguished quotient. It was previously unknown if exceptional p-groups of order less than p ⁶ existed for p an odd prime. The author proved in his M.Sc thesis that there are none of order ≤p ⁴ and gave restrictions on the possible existence of distinguished quotients of exceptional groups of order p ⁵. In this article, an exceptional p-group of order p ⁵ is exhibited for p any odd prime.     

On Long Minimal Zero Sequences in Finite Abelian Groups

Periodica Mathematica Hungarica -     

二次极大子群皆是$PSC^{*}$-群的有限群

This paper discusses the influence of minimal subgroups on the structure of finite groups and gives the structures of finite groups all of whose second maximal subgroups are PSC^＊-groups.     

任意两个非交换元均生成 p3阶子群的有限 p -群

该文分类了任意两个非交换元均生成 p³阶子群的有限 p -群.作为推论, 完全解决了文献[1]中提出的第237个问题: 对于所有的 x,y∈ G, 研究满足条件( x, y) |≤p³的 p -群 G.     

Automorphism Groups of Finite Abelian p-groups and Transvections

We define a particular type of automorphisms called transvections on a finite finite abelian p-group H_p. It is proved that the subgroup E of the automorphism group Aut(H_p) of H_p generated by those transvections is normal in it, and that Aut(H_p) can be written as the product of E and some abelian subgroup K. The center of Aut(H_p) is also determined.     

Finite p-Groups Whose Abelian Subgroups Have a Trivial Intersection

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.     

Finite Abelian Groups of K3 Surfaces with Smooth Quotient

The quotient space of a K3 surface by a finite group is an Enriques surface or a rational surface if it is smooth. Finite groups where the quotient space are Enriques surfaces are known. In this paper, by analyzing effective divisors on smooth rational surfaces, the author will study finite groups which act faithfully on K3 surfaces such that the quotient space are smooth. In particular, he will completely determine effective divisors on Hirzebruch surfaces such that there is a finite Abelian co...     

An Outer Commutator Multiplier and Capability of Finitely Generated Abelian Groups

We present an explicit structure for the Baer invariant of a finitely generated abelian group with respect to the variety [𝔑 _{c 1} , 𝔑 _{c 2} ], for all c ₂ ≤ c ₁ ≤ 2c ₂. As a consequence, we determine necessary and sufficient conditions for such groups to be [𝔑 _{c 1} , 𝔑 _{c 2} ]-capable. We also show that if c ₁ ≠ 1 ≠ c ₂, then a finitely generated abelian group is [𝔑 _{c 1} , 𝔑 _{c 2} ]-capable if and only if it is capable. Finally, we show that 𝔖₂-capability implies capability, but there is a capable finitely generated abelian group which is not 𝔖₂-capable.