AI 中文总结
本文以O'Nan-Scott定理为基础，对素数p对应的p^4阶B群展开分类研究，明确了B群的判定条件，推进了Burnside时期以来相关问题的探究。
AI 中文摘要
若本原置换群G包含同构于H的正则子群时G是双传递的，则称群H为B群。早在William Burnside时代起，已有多位学者研究特定类群是否为B群。本文以O'Nan-Scott定理为出发点，对素数p对应的p^4阶B群进行分类。
英文摘要
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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