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May 20, 2026Hacettepe Journal of Mathematics and StatisticsOpen Access

Sφ-Supplemented and Coprime Action in Finite Groups

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Authors

QLQiang LiuYHYuxi Huang

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Overview

Investigates SΦ-supplement in coprime action, revealing p-nilpotency criteria.

Key Points

  • The aim is to explore SΦ-supplemented subgroups under coprime action and derive p-nilpotency criteria.
  • Defined ASΦ-supplemented subgroups in relation to A-invariant normal subgroups.
  • Examined maximal invariant subgroup structures within Sylow subgroups.
  • Established several criteria for p-nilpotency based on maximal invariant subgroups.
  • Showed that under coprime action, SΦ-supplemented subgroups relate closely to their Sylow subgroup structures.

Cite This Study

Liu et al. (2026) studied this question.

synapsesocial.com/papers/6a0d5089f03e14405aa9c6e4https://doi.org/10.15672/hujms.1823576
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Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

  1. 1Finite groups with weakly $S\Phi$-supplemented minimal subgroups2026
  2. 2A new criterion for p-nilpotency and solvability of finite groups by coprime actions2024
  3. 3A new criterion for <i>p</i> -nilpotency and solvability of finite groups by coprime actions2024 · 5 citations
  4. 4On <i>IC</i> Φ <i> <sub>S</sub> </i> – subgroups of finite groups2024
  5. 5On Π-Normal Subgroups and the p-Supersolvability of Finite Groups2026