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Journals / International Electronic Journal of Algebra / 2026 / Volume: 7 Issue: 7

NEW CRITERIA FOR p-NILPOTENCE OF FINITE GROUPS

Shitian Liu
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Publication Date
2010-06-01
DOI
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AI Summary & Key Takeaways

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

In this paper, we investigate the structure of a finite group G under the assumption that certain subgroups are X-g pronormal, where X = F(G) is the Fitting subgroup of G.

📌 3 Key Takeaways

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Objective & Hypothesis:A subgroup H is X-g pronormal in G if, for H, X ≤ G and g ∈ G, H ∩ X and Hg ∩ X are conjugate in J = hH ∩ X, Hg ∩ Xi.
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Key Findings & Data:A subgroup H is X-g pronormal in G if, for H, X ≤ G and g ∈ G, H ∩ X and Hg ∩ X are conjugate in J = hH ∩ X, Hg ∩ Xi.
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Conclusion & Impact:In this paper, we investigate the structure of a finite group G under the assumption that certain subgroups are X-g pronormal, where X = F(G) is the Fitting subgroup of G.
🔬Design:Article
📍Scope:Comprehensive Sample
⚙️Variables:F(G)-g pronormal subgroups · Sylow p-subgroup · maximal subgroups

Abstract

A subgroup H is X-g pronormal in G if, for H, X ≤ G and g ∈ G, H ∩ X and Hg ∩ X are conjugate in J = hH ∩ X, Hg ∩ Xi. In this paper, we investigate the structure of a finite group G under the assumption that certain subgroups are X-g pronormal, where X = F(G) is the Fitting subgroup of G.

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Cite This Article

Liu, S. (2010). NEW CRITERIA FOR p-NILPOTENCE OF FINITE GROUPS. International Electronic Journal of Algebra, Volume: 7 Issue: 7. https://ajindex.com/articles/1588311

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