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© de Gruyter 2014.It is known that the centralizer of a matrix over a finite field depends, up to conjugacy, only on the type of the matrix, in the sense defined by J. A. Green. In this paper an analogue of the type invariant is defined that in general captures more information; using this invariant the result on centralizers is extended to arbitrary fields. The converse is also proved: thus two matrices have conjugate centralizers if and only if they have the same generalized type. The paper ends with the analogous results for symmetric and alternating groups.
Author(s): Britnell JR, Wildon M
Publication type: Article
Publication status: Published
Journal: Journal of Group Theory
Year: 2014
Volume: 17
Issue: 5
Pages: 875-887
Print publication date: 01/09/2014
Online publication date: 10/01/2014
Acceptance date: 01/01/1900
ISSN (print): 1433-5883
ISSN (electronic): 1435-4446
Publisher: Walter de Gruyter GmbH
URL: https://doi.org/10.1515/jgt-2013-0058
DOI: 10.1515/jgt-2013-0058
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