• Title, Summary, Keyword: exterior centralizers

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COMMUTING ELEMENTS WITH RESPECT TO THE OPERATOR Λ IN INFINITE GROUPS

  • Rezaei, Rashid;Russo, Francesco G.
    • Bulletin of the Korean Mathematical Society
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    • v.53 no.5
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    • pp.1353-1362
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    • 2016
  • Using the notion of complete nonabelian exterior square $G\hat{\wedge}G$ of a pro-p-group G (p prime), we develop the theory of the exterior degree $\hat{d}(G)$ in the infinite case, focusing on its relations with the probability of commuting pairs d(G). Among the main results of this paper, we describe upper and lower bounds for $\hat{d}(G)$ with respect to d(G). Here the size of the second homology group $H_2(G,\mathbb{Z}_p)$ (over the p-adic integers $\mathbb{Z}_p$) plays a fundamental role. A further result of homological nature is placed at the end, in order to emphasize the influence of $H_2(G,\mathbb{Z}_p)$ both on G and $\hat{d}(G)$.