Groups with normal restriction property
published in 'Arch. Math', 2009
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 ∩ M =... more 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 ∩ 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 (1998), 631–638)
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Seen by:Normal restriction in finite groups
published in "Communications in Algebra", 2011
We proved some sufficient conditions for the solvability of finite groups which possess many NR-subgroups. We also... more We proved some sufficient conditions for the solvability of finite groups which possess many NR-subgroups. We also proved a criterion for the existence of a normal p-complement in finite groups.

