𝑀-groups with Sylow towers

Gunter, Elsa L.

doi:10.1090/S0002-9939-1989-0955459-3

$M$-groups with Sylow towers
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by Elsa L. Gunter PDF

Proc. Amer. Math. Soc. 105 (1989), 555-563 Request permission

Abstract:

Let $G$ be a finite group, all of whose irreducible complex characters are induced from linear characters. Suppose that $G$ has a normal series of Hall subgroups ${G_i} \triangleleft G$ such that ${G_0} = 1,{G_n} = G$, and $\left | {{G_i}:{G_{i - 1}}} \right |$ is a power of a prime, for each $i = 1, \ldots ,n$. If $N$ is a normal subgroup of $G$, then every irreducible complex character of $N$ is induced from a linear character.

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