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Journals / International Electronic Journal of Algebra / 2012 / Cilt: 11 - Sayı: 11

A NOTE ON THE p-NILPOTENCY OF A FINITE GROUP

Changwen Lİ
Pages
12–19
Publication Date
2012-06-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We investigate the influence of s-quasinormally embedded and weakly s-supplemented subgroups on the p-nilpotency of a finite group.

📌 3 Key Takeaways

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Objective & Hypothesis:Suppose that G is a finite group and H is a subgroup of G.
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Key Findings & Data:H is said to be s-quasinormally embedded in G if for each prime p dividing |H|, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is called weakly s-supplemented in G if there is a subgroup T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-quasinormal in G.
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Conclusion & Impact:We investigate the influence of s-quasinormally embedded and weakly s-supplemented subgroups on the p-nilpotency of a finite group.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:s-quasinormally embedded · weakly s-supplemented · p-nilpotent

Abstract

Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing |H|, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is called weakly s-supplemented in G if there is a subgroup T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-quasinormal in G. We investigate the influence of s-quasinormally embedded and weakly s-supplemented subgroups on the p-nilpotency of a finite group.

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Cite This Article

Lİ, C. (2012). A NOTE ON THE p-NILPOTENCY OF A FINITE GROUP. International Electronic Journal of Algebra, Cilt: 11 - Sayı: 11, 12–19. https://ajindex.com/articles/832467

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