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http://dx.doi.org/10.4134/BKMS.b150636

COMMUTING ELEMENTS WITH RESPECT TO THE OPERATOR Λ IN INFINITE GROUPS  

Rezaei, Rashid (Department of Mathematics Malayer University)
Russo, Francesco G. (Department of Mathematics and Applied Mathematics University of Cape Town)
Publication Information
Bulletin of the Korean Mathematical Society / v.53, no.5, 2016 , pp. 1353-1362 More about this Journal
Abstract
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 $\hat{d}(G)$.
Keywords
exterior degree; exterior center; exterior centralizers; complete nonabelian exterior square;
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Times Cited By KSCI : 3  (Citation Analysis)
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