Browsing by Author "Rodrigues, Bernardo"

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    A characterization of procyclic groups via complete exterior degree
    (Multidisciplinary Digital Publishing Institute (MDPI), 2024) Rodrigues, Bernardo; Russo, Francesco G
    We describe the nonabelian exterior square (Formula presented.) of a pro-p-group G (with p arbitrary prime) in terms of quotients of free pro-p-groups, providing a new method of construction of (Formula presented.) and new structural results for (Formula presented.). Then, we investigate a generalization of the probability that two randomly chosen elements of G commute: this notion is known as the “complete exterior degree” of a pro-p-group and we will use it to characterize procyclic groups. Among other things, we present a new formula, which simplifies the numerical aspects which are connected with the evaluation of the complete exterior degree