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arXiv · 2608.26463

A Determination of $B$-groups of Order $p^4$

Christopher Herbig
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Abstract

A group $H$ is said to be a $B$-group if whenever a primitive permutation group $G$ contains a regular subgroup isomorphic to $H$, then $G$ is doubly transitive. Going as far back as William Burnside, several authors have investigated whether certain families of groups are $B$-groups. Using the O'Nan-Scott Theorem as our starting point, we classify the $B$-groups of order $p^4$ where $p$ is a prime.

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Christopher Herbig. 2026-08-26. A Determination of $B$-groups of Order $p^4$. https://arxiv.org/abs/2608.26463

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