A characterization of procyclic groups via complete exterior degree
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Date
2024
Journal Title
Journal ISSN
Volume Title
Publisher
Multidisciplinary Digital Publishing Institute (MDPI)
Abstract
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
Description
Keywords
Free profinite groups, Nonabelian exterior square, Pro-p-groups, Schur multiplier
Citation
Rodrigues, B.G. and Russo, F.G., 2024. A Characterization of Procyclic Groups via Complete Exterior Degree. Mathematics, 12(7), p.1018.