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

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    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.
    Original languageEnglish
    Number of pages12
    JournalBULLETIN OF THE MALAYSIAN MATHEMATICAL SOCIETY
    Volumein stampa
    Publication statusPublished - 2013

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