The Open Mathematics Journal

2009, 2 : 36-37
Published online 2009 December 15. DOI: 10.2174/1874117400902010036
Publisher ID: TOMATJ-2-36

The Solubility of the Group of the Form ABA†

Abdullah Al-roqi
Department of Mathematics, College of Science, King Abdulaziz University, P.O.Box 80203, Jeddah 21589, Saudi Arabia.

ABSTRACT

In this paper, we show that if A and B are abelian subgroups of coprime orders and A is self normalizing then G = ABA possesses a normal complement to A. The proof presented here is direct and elementary.