The Influence of the Complete Nonexterior Square Graph on some Infinite Groups

Erwin, David; Russo, Francesco G.

doi:10.1007/s10986-016-9331-2

Cited by 3 publications

(4 citation statements)

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“…This set turns out to be a closed normal subgroup of G by Lemma 3 of [9]. Thirdly, we recall that a pro-p-group P is procyclic, if it is topologically generated by a single element.…”

Section: Introduction and Formulation Of The Main Resultsmentioning

confidence: 98%

“…is a closed subgroup of G, called a complete exterior centralizer of x in G (see [7,9]), and the Haar measure µ on G, whose properties are illustraed by Theorem 2.8 and Exercise E2.3 in [1], allows us to introduce the complete exterior degree…”

Section: Introduction and Formulation Of The Main Resultsmentioning

confidence: 99%

“…In the present section we report some results on the exterior degree in [2,7,9] but also some results of homological algebra in [1,2,16]. Here, [G, G] denotes the closure of the commutator subgroup…”

Section: Some Observations On the Schur Multipliersmentioning

confidence: 99%

“…Example 1. The present example appears in [9], so we report the main information only and a few new computations. Consider the elementary abelian p-group…”

Section: Proofs Of the Main Theoremsmentioning

confidence: 99%

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A Characterization of Procyclic Groups via Complete Exterior Degree

Rodrigues,

Russo

2024

Mathematics

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We describe the nonabelian exterior square G∧^G 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 G∧^G and new structural results for G∧^G. 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.

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“…This set turns out to be a closed normal subgroup of G by Lemma 3 of [9]. Thirdly, we recall that a pro-p-group P is procyclic, if it is topologically generated by a single element.…”

Section: Introduction and Formulation Of The Main Resultsmentioning

confidence: 98%

Section: Introduction and Formulation Of The Main Resultsmentioning

confidence: 99%

Section: Some Observations On the Schur Multipliersmentioning

confidence: 99%

“…Example 1. The present example appears in [9], so we report the main information only and a few new computations. Consider the elementary abelian p-group…”

Section: Proofs Of the Main Theoremsmentioning

confidence: 99%

See 2 more Smart Citations