On multiplication group of an AG-group

M. Shah
DEPARTMENT OF MATHEMATICS, QUAID-I-AZAM UNIVERSTY, ISLAMABAD, PAKISTAN.
A. Ali
DEPARTMENT OF MATHEMATICS, QUAID-I-AZAM UNIVERSTY, ISLAMABAD, PAKISTAN.
I. Ahmad
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF MALAKAND, DIR.
V. Sorge
SCHOOL OF COMPUTER SCIENCE, UNIVERSITY OF BIRMINGHAM, UK.

\(^{1}\)Corresponding Author: email@gmail.com

Copyright © 2015 M. Shah, A. Ali, I. Ahmad, V. Sorge. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Published: December, 2015.

Abstract

We are investigating the multiplication group of a special class of quasigroup called AG-group. We prove some interesting results such as: The multiplication group of an AG-group of order n is a non-abelian group of order 2n and its left section is an abelian group of order n. The inner mapping group of an AG-group of any order is a cyclic group of order 2.

Keywords:

Multiplication group, inner mapping group, translations.