Extra-special p-groups as groups of automorphisms

被引：0

作者：

De Melo, E. ^{[1
]}

Gomes, M. E. ^{[1
]}

Lima, I ^{[1
]}

机构：

[1] Univ Brasilia, Dept Matemat, BR-70910900 Brasilia, DF, Brazil

来源：

COMMUNICATIONS IN ALGEBRA | 2023年 / 51卷 / 02期

关键词：

Automorphisms; p-groups; associated Lie rings; FIXED-POINTS; FINITE;

D O I：

10.1080/00927872.2022.2102178

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let p be a prime and E an extra-special p-group of exponent p and order p(2n+1). Suppose that E acts by automorphisms on a finite p'-group G. We prove that if gamma(n)(C-G(a)) is nilpotent for any a is an element of E-#, then gamma(n)(G) is nilpotent. If, for some integer d such that 2(d)<= n, the dth derived group of C-G(a) is nilpotent for any a is an element of E-#, then the dth derived group G((d)) is nilpotent. We also prove similar results for Lie algebras.

引用

页码：475 / 484

页数：10

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