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Published online by Cambridge University Press: 17 April 2009
In this note we show that if H is any subgroup of the finite group G and if D is a normal subgroup of H such that H/D is soluble and the order of H/D is relatively prime to the index of B in G then the existence of a normal subgroup N of G such that NH = G and N ∩ H is contained in D is equivalent to the condition that every irreducible character of H/D can be extended to one of G. This is a generalization of a result due to Sah for the case when D is the identity subgroup.