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
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
收藏
页码:2931 / 2951
页数:21
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