On identities in matrix groups
type: Item
instance of: scholarly article
title: On identities in matrix groups
zbMATH Open document ID: 0836.20063
DOI: 10.1007/BF03322241
author: Anna Fukshansky
published in: Results in Mathematics
publication date: 1995-10-18T00:00:00Z
review text: It is proved that in the groups \(\text{Gl}(n, K)\), \(\text{Sl} (n,K)\) \((K\) is a finite or infinite field) no nontrivial identity \(A_1 X^{k_1} A_2 X^{k_2} \dots A_m X^{k_m} =1\) holds for all \(X\) in the group, \(A_1, \dots, A_m\) not in the center of the groups -- under the assumption that the cardinality of \(K\) is greater than \(n\) and \(2(k_1 + \cdots + k_m)\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E05
Mathematics Subject Classification ID: 20F05
zbMATH DE Number: 792557
zbMATH Keywords: free subgroups
zbMATH Keywords: linear groups
zbMATH Keywords: identities with parameters
reviewed by: Stanisław Balcerzyk
MaRDI profile type: Publication
cites work: On faithful representations of free products of groups
cites work: Almost all subgroups of a Lie group are free
full work available at URL: https://doi.org/10.1007/bf03322241
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description: scientific article; zbMATH DE number 792557