Finite \(p\)-groups with cyclic commutator subgroup and cyclic center
type: Item
instance of: scholarly article
title: Finite \(p\)-groups with cyclic commutator subgroup and cyclic center
zbMATH Open document ID: 0921.20016
DOI: 10.1007/BF02312775
author: A. A. Finogenov
published in: Mathematical Notes
publication date: 1999-10-03T00:00:00Z
review text: The author classifies the finite \(p\)-groups with cyclic commutator subgroup and cyclic center; for \(p=2\) the condition \([G',G]\subseteq G^{\prime 4}\) is added. It turns out that there are 13 types of such groups when its class \(c(G)\) is greater than 2 (the case \(c(G)=2\) has been settled already by \textit{Y. K. Leong} [J. Aust. Math. Soc., Ser. A 17, 142-153 (1974; Zbl 0286.20022) and 27, 125-140 (1978; Zbl 0402.20018), respectively]). Also all possible cases, when isomorphic groups occur, are listed.
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20F12
zbMATH DE Number: 1262489
zbMATH Keywords: isomorphism problem
zbMATH Keywords: central products
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: cyclic commutator subgroups
zbMATH Keywords: cyclic centers
reviewed by: Gerhard Kowol
MaRDI profile type: Publication
cites work: Odd order nilpotent groups of class two with cyclic centre
cites work: Q4186538
cites work: Finite \(p\)-groups with a cyclic commutator subgroup
cites work: Power automorphisms of a group
description: scientific article; zbMATH DE number 1262489