Answer by Joseph Van Name for How small can maximal subgroups be?
I claim that there are finite groups whose order has arbitrarily many repeating prime factors but which contain a cyclic maximal subgroup of prime order.Let $F$ be a finite field of order $q=p^m$. Let...
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$A_5$ is a maximal subgroup of $\operatorname{\rm PSL}(2,p)$ when $p$ is $\pm 1$ mod $10$. Combining this with Dirichlet's theorem for primes congruent to one modulo $10$ times a highly composite...
View ArticleHow small can maximal subgroups be?
Given a finite group $G$, let $p(G)$ denote the number of prime factorsof the order of $G$ (counting multiplicities).Does there exist a function $f: \mathbb{N} \rightarrow \mathbb{N}$which grows faster...
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