A note on the projective representations of finite groups
type: Item
instance of: scholarly article
title: A note on the projective representations of finite groups
zbMATH Open document ID: 0943.20011
author: Dǎnuţ Marcu
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 2000-06-13T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108504
review text: The author considers projective complex representations of a finite group \(G\) with a given cocycle \(\alpha\). The main result of the paper reads as follows. Let \(P_1,\dots,P_n\) be the Sylow \(p_i\)-subgroups of \(G\), where \(p_1,\dots,p_n\) are the primes dividing the order of \(G\). If \(M_i\) is a subgroup of \(P_i\) of minimal order such that the cohomology class of the restriction of \(\alpha\) to \(M_i\) is trivial, then the greatest common divisor of the degrees of the projective characters of \(G\) with cocycle \(\alpha\) equals \(\prod_{i=1}^n[P_i:M_i]\). Several corollaries are also given.
reviewed by: Andrei Marcus
Mathematics Subject Classification ID: 20C25
Mathematics Subject Classification ID: 20D60
zbMATH DE Number: 1395888
zbMATH Keywords: projective representations
zbMATH Keywords: Schur multipliers
zbMATH Keywords: character degrees
zbMATH Keywords: projective characters
zbMATH Keywords: Sylow subgroups
MaRDI profile type: Publication
cites work: Q3684285
cites work: Projective Representations of Abelian Groups
description: scientific article; zbMATH DE number 1395888