On subgroups and epimorphic images of finite \(p\)-groups
type: Item
instance of: scholarly article
title: On subgroups and epimorphic images of finite \(p\)-groups
zbMATH Open document ID: 0999.20013
published in: Journal of Algebra
publication date: 2002-09-04T00:00:00Z
review text: One of the aims of this paper is a revision of the proofs of several theorems of Blackburn and the author on the structure of finite \(p\)-groups. The proofs are simplified and shortened. Some of the results themselves are generalized and improved. Sections 6 and 7, in particular, can be regarded as a survey, with full proofs, of the most important counting theorems on finite \(p\)-groups. A number of new related results are also proved. The concluding section 16 contains more than 30 open questions on finite \(p\)-groups related to the topics considered in the paper.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D60
Mathematics Subject Classification ID: 20D45
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 1749640
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: regular \(p\)-groups
zbMATH Keywords: \(p\)-groups of maximal class
zbMATH Keywords: metacyclic groups
zbMATH Keywords: automorphisms
zbMATH Keywords: subgroup lattices
zbMATH Keywords: counting theorems
author: Yakov Berkovich
reviewed by: Evgenii I. Khukhro
MaRDI profile type: Publication
full work available at URL: jabr.2001.8790
OpenAlex ID: W2023571735
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DOI: 10.1006/JABR.2001.8790
description: scientific article; zbMATH DE number 1749640