There is no upper bound for the diameter of the commuting graph of a finite group

We construct a family of finite 2-groups which have commuting graph of increasing diameter.     

两类重要p-群及其自同构群的阶

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.     

子群的核平凡或正规闭包极大的有限p群

称有限 p 群 G 为ACT 群,如果对每个交换子群H, 其正规核 H_G=1 或 H_G=H. 又称p 群 G是CC 群,如果对每个非正规交换子群H, 有 H_G=1 或 H^G 在G中的指数为 p. 本文分类了ACT 群和CC 群.     

The K_2-groups over Finaite Commutative Rings

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 and finite 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.     

有限秩的幂零p-群的p-自同构

设G是一个有限秩的幂零p-群,α和β是G的两个p-自同构,记I= ((αβ(g))(βα(g))-1)|g∈G),则(i)当I是有限循环群时,α和β生成一个有限P-群; (ii)当I是拟循环p-群时,α和β生成一个可解的剩余有限P-群,它是有限生成的无挠幂零群被有限p-群的扩张．     

Curran猜想的解答

本文确定了能作为有限群自同构群的Ｐ－群的最佳下最，彻底解决了Ｃｕｒｒａｎ在１９８９年提出的关于此最佳下界的三个猜想。     

On G-Covering Subgroup Systems for Some Saturated Formations of Finite Groups

Let ? be a class of groups and G a finite group. We call a set Σ of subgroups of G a G-covering subgroup system for ? if G ∈ ? whenever Σ ? ?. For a non-identity subgroup H of G, we put Σ _H be some set of subgroups of G which contains at least one supplement in G of each maximal subgroup of H. Let p ≠ q be primes dividing |G|, P, and Q be non-identity a p-subgroup and a q-subgroup of G, respectively. We prove that Σ _P and Σ _P  ∪ Σ _Q are G-covering subgroup systems for many classes of finite groups.     

On Central Automorphisms Fixing the Center Element-Wise

Let G be a finite p-group of nilpotency class 2. We find necessary and sufficient conditions on G such that each central automorphism of G fixes the center of G element-wise.     

On Groups with a CC(n)-Subgroup

A subgroup H of G is a CC(n)-subgroup of G if |G: H| >n and |C_G(x): C_H(x)| ≤n for each element x ∈ H ? {1}. In this article, we study the finite p-groups with a nontrivial CC(p)-subgroup, and the locally nilpotent groups with a nontrivial CC(n)-subgroup.