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18.25 (2014)

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Let $\text{form}(G)$ be the formation generated by a finite group $G$. Suppose that $G$ has a unique composition series $1 \triangleleft G_1 \triangleleft G_2 \triangleleft G$ and the consecutive factors of this series are $\mathbb{Z}_p, X, \mathbb{Z}_q$, where $p$ and $q$ are primes and $X$ is a non-abelian simple group. Is it true that $\text{form}(G)$ has infinitely many subformations if and only if $p = q$?

Contributor: V. P. Burichenko

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