Finite p-groups whose nonnormal subgroups have orders at most p 3

We classify finite p-groups all of whose nonnormal subgroups have orders at most p3, p odd prime. Together with a known result, we completely solved Problem 2279 proposed by Y. Berkovich and Z. Janko in Groups of Prime Power Order, Vol. 3.     

Finite p-groups all of whose non-abelian proper subgroups are metacyclic

In this paper, we classify the finite p-groups all of whose non-abelian proper subgroups are metacyclic and answer a question posed by Berkovich. Received: 22 June 2005     

On groups whose all proper subgroups have Chernikov derived subgroups

We study the groups for which the derived subgroups of all proper subgroups are Chernikov subgroups under condition that they possess a normal system whose factors are locally graduated.     

Finite p-groups all of whose non-abelian proper subgroups are generated by two elements

In this paper, we classify the finite p-groups all of whose non-abelian proper subgroups are generated by two elements.     

Groups whose non-subnormal subgroups have a transitive normality relation

This article investigates the structure of groups in which every subgroup either is subnormal or has a transitive normality relation, with special attention to the case in which subnormal subgroups have bounded defect.     

换位子群为p阶群的有限p-群的自同构群

设G是换位子群为p阶群的有限p-群,确定了AutG的结构,证明了(i)AutG/AutGG≌Zp-1,其中AutGG={α∈AutG|α平凡地作用在G上}.(ii)AutGG/Op(AutG)≌iGL(ni,p)×jSp(2mj,p),其中Op(AutG)是AutG的最大正规p-子群,ni和mj由G惟一确定.     

Finite p-groups all of whose maximal abelian subgroups are soft

A subgroup A of a p-group G is said to be soft in G if CG(A) = A and |NG(A)/A| = p. In this paper we determined finite p-groups all of whose maximal abelian subgroups are soft; see Theorem A and Proposition 2.4.     

特定阶的子群都同构且交换的有限p-群

研究某些子群同构的有限p-群是很有趣的.例如,Hermann和Mann都曾研究过极大子群都同构的有限p-群,但这类群的结构非常复杂,到现在人们都没能给出其分类.研究了特定阶的子群都同构且交换的有限p-群,并给出其分类.     

Finite 2-generator equilibrated p-groups

Following Blackburn, Deaconescu and Mann, a group G is called an equilibrated group if for any subgroups H,K of G with HK = KH, either H≤NG(K) or K≤NG(H). Continuing their work and based on the classification of metacyclic p-groups given by Newman and Xu, we give a complete classification of 2-generator equilibrated p-groups in this note.     

Finite 2-groups all of whose nonabelian subgroups are generated with involutions

In this note we determine finite nonabelian 2-groups G all of whose nonabelian subgroups are generated by involutions and show that such groups must be quasi-dihedral. This solves the problem Nr. 1595 for p = 2 in [1].     

Finite nonabelian p-groups all of whose nonabelian maximal subgroups are either metacyclic or minimal nonabelian

We give here a complete classification of the title groups (Theorem A).     

Finite p-groups with a minimal non-abelian subgroup of index p(Ⅱ)

We classify completely three-generator finite p-groups G such that Ф(G)≤Z(G)and|G′|≤p2.This paper is a part of the classification of finite p-groups with a minimal non-abelian subgroup of index p,and solve partly a problem proposed by Berkovich.     

Finite 2-groups all of whose nonmetacyclic subgroups are generated by involutions

We classify here nonmetacyclic finite 2-groups all of whose nonmetacyclic subgroups are generated by involutions (Theorem 1.1). This solves problem Nr. 710 for p = 2 stated by Y. Berkovich in [1]. For p > 2 the corresponding problem is open. Received: 14 March 2007 Revised: 15 April 2007     

Finite p-groups with automorphism of a special form

Research on finite solvable groups with C-closed invariant subgroups has given rise to groups structured as follows. Let p, q₁, q₂, ..., q_m be distinct primes, n_i be the exponent of p modulo q_i, and n be the exponent of p modulo . Then G = Pλ〈x〉, where P is a group and ; Z_i; here, Z_i and P/Z(P) are elementary Abelian groups of respective orders and pⁿ, |x| = r, the element x acts irreducibly on P/Z(P) and on each of the subgroups Z_i, and . We state necessary and sufficient conditions for such groups to exist. __________ Translated from Algebra i Logika, Vol. 45, No. 4, pp. 379–389, July–August, 2006.     

n-极大子群为共轭可换的有限群

群G的子群H称为G的共轭可换子群,若HHg=HgH,对任意g∈G都成立,本文考查了n-极大子群为共轭可换时对有限群构造的影响.