Finite p-groups with normal normalisers

Elizabeth A. Ormerod; Gemma Parmeggiani

doi:10.1017/s0004972700034341

Finite p-groups with normal normalisers

Elizabeth A. Ormerod^*
, Gemma Parmeggiani

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the class N of groups in which the normaliser of every subgroup is normal, and the class C of groups in which the commutator subgroup normalises every subgroup. It is clear that C ⊆ N, and it is known that groups in the class N are nilpotent of class at most 3. We show that every finite p-group in N is also in C, provided that p ≥ 5, and we give an example showing that this is not true for p = 2.

Original language	English
Pages (from-to)	141-150
Number of pages	10
Journal	Bulletin of the Australian Mathematical Society
Volume	69
Issue number	1
DOIs	https://doi.org/10.1017/s0004972700034341
Publication status	Published - Feb 2004

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title = "Finite p-groups with normal normalisers",

abstract = "We consider the class N of groups in which the normaliser of every subgroup is normal, and the class C of groups in which the commutator subgroup normalises every subgroup. It is clear that C ⊆ N, and it is known that groups in the class N are nilpotent of class at most 3. We show that every finite p-group in N is also in C, provided that p ≥ 5, and we give an example showing that this is not true for p = 2.",

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AB - We consider the class N of groups in which the normaliser of every subgroup is normal, and the class C of groups in which the commutator subgroup normalises every subgroup. It is clear that C ⊆ N, and it is known that groups in the class N are nilpotent of class at most 3. We show that every finite p-group in N is also in C, provided that p ≥ 5, and we give an example showing that this is not true for p = 2.

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DO - 10.1017/s0004972700034341

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JO - Bulletin of the Australian Mathematical Society

JF - Bulletin of the Australian Mathematical Society

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Finite p-groups with normal normalisers

Abstract

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