Primitive characters of subgroups of 𝑀-groups

Lewis, Mark

doi:10.1090/S0002-9939-97-03625-3

Primitive characters of subgroups of $M$-groups
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by Mark L. Lewis PDF

Proc. Amer. Math. Soc. 125 (1997), 27-33 Request permission

Abstract:

Let $G$ be an $M$–group, let $S$ be a subnormal subgroup of $G$, and let $H$ be a Hall subgroup of $S$. If the character $\gamma \in \operatorname {Irr} {H}$ is primitive, then $\gamma (1)$ is a power of 2. Furthermore, if $|G:S|$ is odd, then $\gamma (1)=1$.

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