A short note on a paper of Gao et al.

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发表日期：

2026年1月15日

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Haoran Yu,
Jian Sun,
Xiaowei Xu

摘要

In this short note, we show that for a normal subgroup H of a Sylow p-subgroup P of a finite group G and for a p-sylowizer S of H in G, $S\cap O^{p}(G)$ $S \cap O^{p} (G)$ is s-permutable in G if and only if $S\cap O^{p}(G)$ $S \cap O^{p} (G)$ is normal in G. Then we derive some main results of Gao et al. (Indian J. Pure Appl. Math 56(4): 1734–1740, 2025) as immediate corollaries from our previous theorem (Arch. Math. (Basel) 118(1): 13–17, 2022).