Nearly ${\varvec{SS}}$-embedded and ${\varvec{SS}}$-supplemented elements in the subset $\varvec{\mathfrak {F_{(\textrm{P,G})}}}$ of finite groups

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2026年4月21日

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Yanhui Xiang,
Jia Zhang,
Liyu Zhu

摘要

As is well known, generalized normalities and supplementarities of all maximal subgroups of a Sylow p-subgroup P are closely related to the structure of a finite group. Viewing from the point of “all”, we construct a set $\mathfrak {F_{(\textrm{P,G})}}=\{{P_{1}<\cdot P|P\cap O^{p}(G)\nleq P_{1}}\}$ $F_{(P,G)} = {P_{1} < \cdot P | P \cap O^{p} (G) ≰ P_{1}}$ which consists of “some” maximal subgroups of P instead of “all”. Further, we investigate the influence of nearly SS-embedded and SS-supplemented properties of its elements on the p-supersolvability of a group. To some extent, our results also improved some Theorems.

Nearly \({\varvec{SS}}\)-embedded and \({\varvec{SS}}\)-supplemented elements in the subset \(\varvec{\mathfrak {F_{(\textrm{P,G})}}}\) of finite groups

摘要