A note on solvability of finite groups

Authors

  • Rola Asaad Hijazi

DOI:

https://doi.org/10.24297/jam.v10i7.1772

Keywords:

Sylow subgroup, c-normal subgroup, c-supplement subgroup, solvable group, supersolvable group.

Abstract

Let G be a finite group. A subgroup H of G is said to be c-normal in G if there exists a normal subgroup K of G such that G = HK and Hg1.jpg K -<HG, where HG is the largest normal subgroup of G contained in H. In this note we prove that if every Sylow subgroup P of G has a subgroup D such that 1 <|D|<|P| and all subgroups H of P with |H|=|D|are c-normal (S-permutable) in G, then G is solvable. This results improve and extend classical and recent results in the literature.

Downloads

Download data is not yet available.

Downloads

Published

2015-05-06

How to Cite

Hijazi, R. A. (2015). A note on solvability of finite groups. JOURNAL OF ADVANCES IN MATHEMATICS, 10(7), 3639–3641. https://doi.org/10.24297/jam.v10i7.1772

Issue

Section

Articles