On the Exterior Degree of the Wreath Product of Finite Abelian Groups

The exterior degree d^(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^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