The exterior degree $d^\wedge(G)$ of a finite group $G$ has been recently introduced by Rezaei and Niroomand in order to study the probability that two given elements $x$ and $y$ of $G$ commute in the nonabelian exterior square $G \wedge G$. This notion is related with the probability $d(G)$ that two elements of $G$ commute in the usual sense. Motivated by a paper of Erovenko and Sury of 2008, we compute the exterior degree of a group which is the wreath product of two finite abelian $p$--groups ($p$ prime). We find some numerical inequalities and study mostly abelian $p$-groups.
|Number of pages||12|
|Journal||BULLETIN OF THE MALAYSIAN MATHEMATICAL SOCIETY|
|Publication status||Published - 2013|