ON p-GROUPS WITH AUTOMORPHISM GROUPS RELATED TO THE CHEVALLEY GROUP G2(p)

被引：1

作者：

Bamberg, John ^{[1
]}

Freedman, Sauld D. ^{[1
,2
]}

Morgan, Luke ^{[1
,3
,4
]}

机构：

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

[2] Univ St Andrews, Sch Math & Stat, St Andrews KY16 9SS, Fife, Scotland

[3] Univ Primorska, UP FAMNIT, Glagoljaska 8, Koper 6000, Slovenia

[4] Univ Primorska, UP IAM, Muzejski Trg 2, Koper 6000, Slovenia

来源：

JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2020年 / 108卷 / 03期

基金：

澳大利亚研究理事会;

关键词：

p-group; exterior square; G(2)(q); MAXIMAL-SUBGROUPS;

D O I：

10.1017/S1446788719000466

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be an odd prime. We construct a p-group P of nilpotency class two, rank seven and exponent p, such that Aut(P) induces N-GL(7;p)(G2(p)) = Z(GL(7; p))G2(p) on the Frattini quotient P=Phi(P). The constructed group P is the smallest p-group with these properties, having order p(14), and when p = 3 our construction gives two nonisomorphic p-groups. To show that P satisfies the specified properties, we study the action of G(2)(q) on the octonion algebra over F-q, for each power q of p, and explore the reducibility of the exterior square of each irreducible seven-dimensional F-q[G2(q)]-module.

引用

页码：321 / 331

页数：11

共 17 条

[1]

[Anonymous], 2009, Graduate Texts in Mathematics

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