Journal of Prime Research in Mathematics

# 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.
DEPARTMENT OF MATHEMATICS, UNIVERSITY OF MALAKAND, DIR.
V. Sorge
SCHOOL OF COMPUTER SCIENCE, UNIVERSITY OF BIRMINGHAM, UK.

$$^{1}$$Corresponding Author: email@gmail.com

### 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.