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ON THE GENUS OF A FINITE CLASSICAL GROUP

Published online by Cambridge University Press:  01 March 1997

MARTIN W. LIEBECK  and
CHRIS WAYMAN PURVIS
MARTIN W. LIEBECK
Affiliation:
Imperial College, London SW7 2BZ
CHRIS WAYMAN PURVIS
Affiliation:
Imperial College, London SW7 2BZ
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Abstract

Let G be a finite group acting faithfully and transitively on a set Ω of size m, and let E = {x1, …, xk} be a generating set for G with x1x2…xk = 1. If x∈G has cycles oflength r1, …, rl in its action on Ω, define ind (x) = [sum ]l1(ri−1).Then the genus g = g(G, Ω, E) is defined by

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Information

Type
Research Article
Information
Bulletin of the London Mathematical Society , Volume 29 , Issue 2 , March 1997 , pp. 159 - 164
Copyright
© The London Mathematical Society 1997

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