Abstract
Let G be a finite group having a normal Hall subgroup H, let K be a field, and let T be an irreducible (linear) K-representation of H of degree deg T whose character is invariant under the action of G. We say that T is extendible to G if there exists a K-representation S of G such that S(h) = T(h) for all hCH. In [5, Theorem 6] Gallagher proved that T is extendible if K is the field of complex numbers. The case when K is an arbitrary field of characteristic zero is treated by Isaacs in [7]. In this note we show that the arguments in Isaacs' paper can be extended to yield the following result:
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