John R Britnell
Cycle index methods for finite groups of orthogonal type in odd characteristic
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 &OHgr;± (d, q), the commutator subgroup of &Ogr;±(d, q). Subsequently we shall look at groups G in the range ![]()
where &Pgr; is the group of non-zero scalars.
Journal of Group Theory, Walter de Gruyter
Print ISSN: 1433-5883
Volume: 9, 11/2006
Pages: 753 - 773
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