Volume 37 • Number 1 • 2014   • On the Exterior Degree of the Wreath Product\\ of Finite Abelian Groups Ahmad Erfanian, Fadila Normahia Abd Manaf, Francesco G. Russo and Nor Haniza Sarmin Abstract. 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. 2010 Mathematics Subject Classification: Primary 20J99; Secondary 20D15, 20P05 Full text: PDF