On coclass and trivial Schur multiplicator.
type: Item
instance of: scholarly article
title: On coclass and trivial Schur multiplicator.
zbMATH Open document ID: 1196.20020
author: M. F. Newman
published in: Journal of Algebra
publication date: 2009-10-02T00:00:00Z
review text: Recall, a \(p\)-group of order \(p^n\) and nilpotency class \(c\) has coclass \(r=n-c\). In [J. Algebra 322, No. 3, 741-751 (2009; Zbl 1196.20019)] \textit{B. Eick} conjectures that, for odd \(p\), the order of a \(p\)-group with trivial Schur multiplicator and coclass \(r\) is bounded by a function \(b(r)\) which is independent of \(p\). In the paper under review this conjecture is confirmed for coclass 2. In particular, the author shows that, for odd prime \(p\), a \(p\)-group with coclass 2 and trivial Schur multiplicator has nilpotency class at most 6.
reviewed by: Rachel D. Camina
Mathematics Subject Classification ID: 20D15
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 5610511
zbMATH Keywords: finite \(p\)-groups
zbMATH Keywords: Schur multiplicators
zbMATH Keywords: coclasses
zbMATH Keywords: nilpotency classes
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2009.04.033
OpenAlex ID: W2046835733
cites work: Computing \(p\)-groups with trivial Schur multiplicator.
cites work: The Groups of Order p 6 (p and Odd Prime)
cites work: Q4544915
DOI: 10.1016/J.JALGEBRA.2009.04.033
description: scientific article; zbMATH DE number 5610511