ON THE NORMALISERS OF ALL NON- p -NILPOTENT SUBGROUPS IN A FINITE GROUP

Xuan Li; Junxin Wang; Xiuyun Guo

doi:10.1017/s0004972725100683

November 28, 2025Bulletin of the Australian Mathematical SocietyOpen Access

ON THE NORMALISERS OF ALL NON- p -NILPOTENT SUBGROUPS IN A FINITE GROUP

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Key Points

Analysis demonstrates the influence of normalisers on finite groups, particularly in relation to subgroup structures.
Key properties of normalisers impact the p-nilpotency of finite groups, with potential implications for group theory.
Investigation focuses on non-p-nilpotent subgroups, emphasizing their role within the broader context of finite groups.
Finding sheds light on how properties of normalisers may affect group behavior and subgroup dynamics.

Implication

Analysis reveals the properties of normalisers affecting finite groups, indicating impacts on subgroup structures based on p-nilpotency.

Abstract

For a prime p , let Nₚ(G) denote the intersection of the normalisers of all non- p -nilpotent subgroups of a finite group G and set Nₚ(G)=G if G itself is p -nilpotent. We give some properties of Nₚ(G) and investigate the influence of Nₚ(G) on G .

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Cite This Study

Li et al. (2025) studied this question.

synapsesocial.com/papers/692e3d846c9b3ab28c18731b https://doi.org/10.1017/s0004972725100683

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ON THE NORMALISERS OF ALL NON- p -NILPOTENT SUBGROUPS IN A FINITE GROUP

Key Points

Implication

Abstract

Discussion

Cite This Study

ON THE NORMALISERS OF ALL NON- p -NILPOTENT SUBGROUPS IN A FINITE GROUP

Key Points

Implication

Abstract

Discussion

Cite This Study

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