Rodrigues, BernardoRusso, Francesco G2025-01-212025-01-212024Rodrigues, B.G. and Russo, F.G., 2024. A Characterization of Procyclic Groups via Complete Exterior Degree. Mathematics, 12(7), p.1018.https://doi.org/10.3390/math12071018https://hdl.handle.net/10566/19886We 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 degreeenFree profinite groupsNonabelian exterior squarePro-p-groupsSchur multiplierArticle