Quotients of permutation groups

Research Report MRR97-051

Quotients of permutation groups

John Cossey

Abstract: If G is a finite permutation group of degree d and N is a normal subgroup of G, Derek Holt [1] has given conditions which show that in some important special cases the least degree of a faithful permutation representation of the quotient G/N will be no larger than d. His conditions do not apply in all cases of interest and he remarks that it would be interesting to know if G/F(G) has a faithful representation of degree no larger than d (where F(G) is the Fitting subgroup of G). We prove in this note that this is the case.

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