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Journal of Group Theory

Editor-in-Chief: Wilson, John S.

Managing Editor: Howie, James / Kramer, Linus / Parker, Christopher W.

Editorial Board Member: Abért, Miklós / Borovik, Alexandre V. / Boston, Nigel / Bridson, Martin R. / Caprace, Pierre-Emmanuel / Giovanni, Francesco / Guralnick, Robert / Jaikin Zapirain, Andrei / Kessar, Radha / Khukhro, Evgenii I. / Kochloukova, Dessislava H. / Malle, Gunter / Olshanskii, Alexander / Remy, Bertrand / Robinson, Derek J.S. / Willis, George

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Cycle index methods for finite groups of orthogonal type in odd characteristic

Citation Information: Journal of Group Theory. Volume 9, Issue 6, Pages 753–773, ISSN (Online) 1435-4446, ISSN (Print) 1433-5883, DOI: 10.1515/JGT.2006.048, February 2007

Publication History

Received:
2005-12-08
Revised:
2006-02-17
Published Online:
2007-02-12

Abstract

This is the third in a series of papers whose object is to show how cycle index methods for finite classical groups, developed by Fulman [Jason Fulman. Cycle indices for the classical groups. J. Group Theory 2 (1999), 251–289.], may be extended to other almost simple groups of classical type. In [John R. Britnell. Cyclic, separable and semisimple transformations in the special unitary groups over a finite field. J. Group Theory 9 (2006), 547–569.] we treated the special unitary groups, and in [John R. Britnell. Cyclic, separable and semisimple transformations in the finite conformal groups. J. Group Theory 9 (2006), 571–601.] the general symplectic and general orthogonal groups. In this paper we shall treat various subgroups of the general orthogonal group over a field of odd characteristic. We shall focus at first on Ω± (d, q), the commutator subgroup of Ο±(d, q). Subsequently we shall look at groups G in the range

where Π is the group of non-zero scalars.

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