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Primitive characters of subgroups of -groups
Authors:Mark L Lewis
Institution:Department of Mathematics, 400 Carver Hall, Iowa State University, Ames, Iowa 50011
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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