Symmetric powers of representations of finite groups
type: Item
instance of: scholarly article
title: Symmetric powers of representations of finite groups
zbMATH Open document ID: 0828.20002
published in: Journal of Algebra
publication date: 1993-05-16T00:00:00Z
review text: The main result is that if \(V\) is a finite dimensional faithful module for a finite group \(G\) over a field \(K\) and \(c\) is the number of elements of \(G\) which have scalar action on \(V\) then, for large values of \(n\), the sum of \(c\) consecutive symmetric powers \(S_n(V) \oplus S_{n + 1} (V) \oplus \cdots \oplus S_{n + c - 1} (V)\) is close to being a free \(KG\)- module. A similar result holds for metabelian Lie powers.
Mathematics Subject Classification ID: 20C05
Mathematics Subject Classification ID: 20C15
zbMATH DE Number: 168591
zbMATH Keywords: finite dimensional faithful modules
zbMATH Keywords: finite groups
zbMATH Keywords: symmetric powers
zbMATH Keywords: free \(KG\)-modules
zbMATH Keywords: metabelian Lie powers
author: Roger M. Bryant
MaRDI profile type: Publication
full work available at URL: jabr.1993.1023
OpenAlex ID: W2066352040
DOI: 10.1006/JABR.1993.1023
description: scientific article; zbMATH DE number 168591