Groups with normal restriction property

Hung P. Tong-Viet

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arXiv · 0912.0865

Groups with normal restriction property

Hung P. Tong-Viet

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Abstract

Let G be a finite group. A subgroup M of G is said to be an NR-subgroup if, whenever K is normal in M, then K^G\cap M=K, where K^G is the normal closure of K in G. Using the Classification of Finite Simple Groups, we prove that if every maximal subgroup of G is an NR -subgroup then G is solvable. This gives a positive answer to a conjecture posed in Berkovich (Houston J Math 24:631-638, 1998).

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Hung P. Tong-Viet. 2009-12-04. Groups with normal restriction property. https://arxiv.org/abs/0912.0865

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