On maximal and Sylow subgroups of finite solvable groups.
type: Item
instance of: scholarly article
title: On maximal and Sylow subgroups of finite solvable groups.
zbMATH Open document ID: 1035.20015
DOI: 10.1023/A:1012389005374
author: E. E. Gribovskaya
author: V. S. Monakhov
published in: Mathematical Notes
publication date: 2003-06-15T00:00:00Z
review text: Let \(G\) be a finite group. \(G\) is said to be bicyclic if it is the product of two cyclic subgroups. The structure of a finite solvable group with bicyclic Sylow subgroups is studied. In particular, it is proved that the nilpotent length of these groups is not greater than 4. Since in any finite solvable group the index of each maximal subgroup is a prime power the structure of a finite solvable group with the index of each maximal subgroup either a prime or the square of a prime or the cube of a prime is studied also. It is proved that the supersolvable coradical of \(G\) is an extension of a metanilpotent group by a 2-group and the nilpotent length of such a group does not exceed 5.
Mathematics Subject Classification ID: 20D10
Mathematics Subject Classification ID: 20D20
Mathematics Subject Classification ID: 20E28
Mathematics Subject Classification ID: 20D40
zbMATH DE Number: 1927787
zbMATH Keywords: finite solvable groups
zbMATH Keywords: Sylow subgroups
zbMATH Keywords: Fitting subgroups
zbMATH Keywords: bicyclic groups
zbMATH Keywords: nilpotent lengths
zbMATH Keywords: derived lengths
zbMATH Keywords: Ore dispersive subgroups
zbMATH Keywords: maximal subgroups
reviewed by: N. M. Kurnosenko
MaRDI profile type: Publication
full work available at URL: a:1012389005374
OpenAlex ID: W175014269
description: scientific article; zbMATH DE number 1927787