Maximal linear groups induced on the Frattini quotient of a p-group

被引：5

作者：

Bamberg, John ^{[1
]}

Glasby, S. P. ^{[1
,3
]}

Morgan, Luke ^{[1
]}

Niemeyer, Alice C. ^{[2
]}

机构：

[1] Univ Western Australia, Ctr Math Symmetry & Computat, 35 Stirling Highway, Crawley 6009, Australia

[2] Rhein Westfal TH Aachen, Lehrstuhl Math B, Lehr & Forsch Gebiet Algebra, Templergraben 64, D-52062 Aachen, Germany

[3] Univ Canberra, Dept Math, Canberra, ACT 2601, Australia

来源：

JOURNAL OF PURE AND APPLIED ALGEBRA | 2018年 / 222卷 / 10期

基金：

澳大利亚研究理事会;

关键词：

FINITE CLASSICAL-GROUPS; AUTOMORPHISM GROUP; NILPOTENT GROUPS; SUBGROUPS; ORDERS;

D O I：

10.1016/j.jpaa.2017.11.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let p > 3 be a prime. For each maximal subgroup H <= GL(d,p) with |H| >= p3d+1(, we) (construct a d-generator finite p-group G with the property that Aut(G)) induces H on the Frattini quotient G/Phi(G) and |G| <= p(d4/2). A significant feature of this construction is that |G| is very small compared to |H|, shedding new light upon a celebrated result of Bryant and Kovacs. The groups G that we exhibit have exponent p, and of all such groups G with the desired action of H on G/Phi(G), the construction yields groups with smallest nilpotency class, and in most cases, the smallest order. (C) 2017 Elsevier B.V. All rights reserved.

引用

页码：2931 / 2951

页数：21

共 31 条

[1] ON THE MAXIMAL-SUBGROUPS OF THE FINITE CLASSICAL-GROUPS [J].