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Rigid Embedding of Simple Groups in the General Linear Group

Published online by Cambridge University Press:  20 November 2018

John D. Dixon
John D. Dixon*
Affiliation:
Carleton University, Ottawa, Ontario
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Abstract

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Let K be a (commutative) field and n be a positive integer. Consider the K-algebra E = Mat (n, K) of all n X n matrices over K, and the corresponding general linear group GL(n, K). We shall define the set R of rigid mappings of E to consist of all a in GLK(E) which can be written in one of two possible forms: either xσ= axb for all x ϵ E or xσ = ax'b for all x ϵ E (where a and b are fixed elements of GL(n, K) and x’ denotes the transpose of x).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 29 , Issue 2 , 01 April 1977 , pp. 384 - 391
Copyright
Copyright © Canadian Mathematical Society 1977

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