Largeness and equational probability in groups

Jaber, Khaled; Wagner, Frank O.

doi:10.5802/ambp.388

Jaber, Khaled ¹ ; Wagner, Frank O.²

¹ Department of Mathematics Faculty of Sciences Lebanese University, Lebanon
² Université de Lyon; Université Lyon 1 CNRS UMR 5208, Institut Camille Jordan 21 avenue Claude Bernard 69622 Villeurbanne-cedex, France

Annales mathématiques Blaise Pascal, Tome 27 (2020) no. 1, pp. 1-17.

Résumé

We define $k$ -genericity and $k$ -largeness for a subset of a group, and determine the value of $k$ for which a $k$ -large subset of $G^{n}$ is already the whole of $G^{n}$ , for various equationally defined subsets. We link this with the inner measure of the set of solutions of an equation in a group, leading to new results and/or proofs in equational probabilistic group theory.

Publié le : 2020-08-26

DOI : 10.5802/ambp.388

Classification : 20A15, 03C60, 20P99
Mots clés : probabilistic group theory, largeness

Affiliations des auteurs :

Jaber, Khaled ¹ ; Wagner, Frank O. ²

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Jaber, Khaled; Wagner, Frank O. Largeness and equational probability in groups. Annales mathématiques Blaise Pascal, Tome 27 (2020) no. 1, pp. 1-17. doi : 10.5802/ambp.388. http://www.numdam.org/articles/10.5802/ambp.388/

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