Groups with normal restriction property
Group Theory
2009-12-07 v1
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).
Cite
@article{arxiv.0912.0865,
title = {Groups with normal restriction property},
author = {Hung P. Tong-Viet},
journal= {arXiv preprint arXiv:0912.0865},
year = {2009}
}
Comments
5 pages