TY - JOUR

T1 - On the exterior degree of the wreath product of finite abelian groups

AU - Russo, Francesco

PY - 2013

Y1 - 2013

N2 - 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.

AB - 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.

UR - http://hdl.handle.net/10447/76437

UR - http://www.emis.de/journals/BMMSS/accepted_papers.htm

M3 - Article

VL - in stampa

JO - Bulletin of the Malaysian Mathematical Sciences Society

JF - Bulletin of the Malaysian Mathematical Sciences Society

SN - 0126-6705

ER -