Commutativity pattern of finite non-abelian $p$-groups determine their orders

Details Commutativity pattern of finite non-abelian $p$-groups determine their orders Commutativity pattern of finite non-abelian $p$-groups determine their orders

2011-09-23

arxiv.org/abs/1109.5007v1

Mathematics

Group Theory

to appear in Communications in Algebra

Scientific paper

Let $G$ be a non-abelian group and $Z(G)$ be the center of $G$. Associate a graph $\Gamma_G$ (called non-commuting graph of $G$) with $G$ as follows: take $G\setminus Z(G)$ as the vertices of $\Gamma_G$ and join two distinct vertices $x$ and $y$, whenever $xy\neq yx$. Here, we prove that "the commutativity pattern of a finite non-abelian $p$-group determine its order among the class of groups"; this means that if $P$ is a finite non-abelian $p$-group such that $\Gamma_P\cong \Gamma_H$ for some group $H$, then $|P|=|H|$.

Affiliated with

Also associated with

No associations

Rating

Commutativity pattern of finite non-abelian $p$-groups determine their orders does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Commutativity pattern of finite non-abelian $p$-groups determine their orders, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Commutativity pattern of finite non-abelian $p$-groups determine their orders will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-724035