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Finite p-groups with normal normalisers
Published online by Cambridge University Press: 17 April 2009
Extract
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.
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 69 , Issue 1 , February 2004 , pp. 141 - 150
- Copyright
- Copyright © Australian Mathematical Society 2004