ON THE GROUPS WITH THE PARTICULAR NON-COMMUTING GRAPHS

Document Type : Original Manuscript

Authors

Department of pure Mathematics, Shahrekord University, P.O.Box 115, Shahrekord, Iran.

Abstract

Let

G

be a non-abelian finite group. In this paper, we prove that

G a m m a (G)

K_{4}

-free if and only if

G c o n g A t i m e s P

, where

A

is an abelian group,

P

is a

2

-group and

G / Z (G) c o n g m a t h b b Z_{2} t i m e s m a t h b b Z_{2}

. Also, we show that

G a m m a (G)

K_{1, 3}

-free if and only if

G c o n g {m a t h b b S}_{3}, D_{8}

Q_{8}

Keywords