The Fischer-Clifford matrices of a maximal subgroup of

Authors:
Faryad Ali and Jamshid Moori

Journal:
Represent. Theory **7** (2003), 300-321

MSC (2000):
Primary 20C15, 20D08, 20E22

DOI:
https://doi.org/10.1090/S1088-4165-03-00175-4

Published electronically:
July 29, 2003

MathSciNet review:
1993362

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The Fischer group is the largest sporadic simple Fischer group of order

The group is the derived subgroup of the Fischer -transposition group discovered by Bernd Fischer. There are five classes of elements of order 3 in as represented in ATLAS by , , , and . A subgroup of of order is called of type , where , if it is generated by an element in the class . There are six classes of maximal 3-local subgroups of as determined by Wilson. In this paper we determine the Fischer-Clifford matrices and conjugacy classes of one of these maximal 3-local subgroups , where is the natural orthogonal module for with subgroups of type corresponding to the totally isotropic points. The group is a nonsplit extension of by .

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Additional Information

**Faryad Ali**

Affiliation:
School of Mathematics, Statistics and I.T., University of Natal, Private Bag X 01, Scottsville, Pietermaritzburg 3209, South Africa

**Jamshid Moori**

Affiliation:
School of Mathematics, Statistics and I.T., University of Natal, Private Bag X 01, Scottsville, Pietermaritzburg 3209, South Africa

DOI:
https://doi.org/10.1090/S1088-4165-03-00175-4

Received by editor(s):
August 29, 2002

Received by editor(s) in revised form:
April 7, 2003

Published electronically:
July 29, 2003

Additional Notes:
The first author was supported by a postgraduate bursary from the NRF(SA)

The second author was supported by a research grant from University of Natal and NRF(SA)

Article copyright:
© Copyright 2003
American Mathematical Society