Profinite groups with abelian Sylow subgroups

被引：0

作者：

Lopes, Lucas C. ^{[1
,2
]}

Shumyatsky, Pavel ^{[1
]}

Zalesskii, Pavel A. ^{[1
]}

机构：

[1] Univ Brasilia, Dept Matemat, Brasilia, DF, Brazil

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

来源：

COMMUNICATIONS IN ALGEBRA | 2024年 / 52卷 / 01期

关键词：

Abelian; finite rank; profinite groups; Sylow subgroups;

D O I：

10.1080/00927872.2023.2239352

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We extend the definition of a finite A-group to profinite groups and give a description of profinite A-groups as a triple semidirect product of two prosoluble groups with a semisimple group, extending an old result of A. M. Broshi to the profinite case. We also prove that a profinite A-group with finitely generated non-trivial Fitting subgroup is metabelian-by-(finite exponent). If, in addition, G is finitely generated then it is virtually metabelian polycyclic.Communicated by Mandi Schaeffer Fry

引用

页码：224 / 232

页数：9

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