The structure of \(p\)-groups of finitary transformations
type: Item
instance of: scholarly article
title: The structure of \(p\)-groups of finitary transformations
zbMATH Open document ID: 0829.20066
DOI: 10.1007/BF02259823
author: V. V. Belyaev
published in: Algebra and Logic
publication date: 1994-04-12T00:00:00Z
review text: A linear transformation of a vector space is called finitary if it acts trivially on some subspace of finite codimension. Clearly, the set of all invertible finitary transformations of a space \(V\), denoted \(\text{FGL} (V)\), is a normal subgroup of the linear group \(\text{GL}(V)\). When \(V\) has finite dimension, it is evident that \(\text{FGL} (V) = \text{GL} (V)\), but for infinite-dimensional \(V\), \(\text{FGL}(V)\) is a proper subgroup of \(\text{GL} (V)\). \(G\) is called a finitary transformation group whenever it is embeddable in \(\text{FGL} (V)\) for some vector space \(V\). In the present paper, we concentrate on the structure of \(p\)- groups of finitary transformations over a field of characteristic \(\neq p\).
Mathematics Subject Classification ID: 20G15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20F50
zbMATH DE Number: 536674
zbMATH Keywords: invertible finitary transformations
zbMATH Keywords: linear groups
zbMATH Keywords: finitary transformation groups
zbMATH Keywords: \(p\)-groups of finitary transformations
MaRDI profile type: Publication
cites work: Infinite alternating groups as finitary linear transformation groups
cites work: The structure of groups of finitary transformations
cites work: Q3667072
cites work: A question of L. A. Shemetkov
description: scientific article; zbMATH DE number 536674