与有限群元素阶的和相关的两个新函数
Two new functions related to the sum of element orders of a finite group
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中文总结 AI 辅助
针对有限群及其真正规子群，引入两个涉及元素阶之和的新函数并证明其满足特定不等式，明确等号成立的条件。
中文摘要 AI 辅助
设G为有限群，H为G的真正规子群。本文引入两个新函数o(G,H)和ψ''(G,H)，涉及G与H的元素阶之和，证明它们满足特定不等式，等号成立当且仅当(G,H)为特定类型的等阶对。
英文摘要
Let $G$ be a finite group and $H$ be a proper normal subgroup of $G$. In this note, we introduce two new functions $o(G,H)$ and $ψ''(G,H)$ involving the sums of element orders of $G$ and $H$. We prove that they satisfy certain inequalities, with equality if and only if $(G,H)$ is an equal order pair of a particular type.
