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Journal of Group Theory

Editor-in-Chief: Parker, Christopher W. / Wilson, John S.

Managing Editor: Howie, James / Khukhro, Evgenii I. / Kramer, Linus

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Certain classical groups are not well-defined

John N. Bray1 / Derek F. Holt2 / Colva M. Roney-Dougal3

1School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London E1 4NS, U.K. E-mail:

2Mathematics Institute, University of Warwick, Coventry CV4 7AL, U.K. E-mail:

3School of Mathematics and Statistics, North Haugh, St Andrews, Fife KY16 9SS, U.K. E-mail:

Citation Information: Journal of Group Theory. Volume 12, Issue 2, Pages 171–180, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/JGT.2008.069, November 2008

Publication History

Published Online:


In this article we show that the isomorphism type of certain semilinear classical groups may depend on the choice of form matrix, as well as the dimension and the field size. When there is more than one isomorphism type, we count them and present effective polynomial-time algorithms to determine whether two such groups are isomorphic.

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