English

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).

Keywords

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

R2 v1 2026-06-21T14:19:40.726Z