Largeness and equational probability in groups
Annales mathématiques Blaise Pascal, Volume 27 (2020) no. 1, pp. 1-17.

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.

Published online:
DOI: 10.5802/ambp.388
Classification: 20A15,  03C60,  20P99
Keywords: probabilistic group theory, largeness
Khaled Jaber 1; Frank O. Wagner 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
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Khaled Jaber; Frank O. Wagner. Largeness and equational probability in groups. Annales mathématiques Blaise Pascal, Volume 27 (2020) no. 1, pp. 1-17. doi : 10.5802/ambp.388. https://ambp.centre-mersenne.org/articles/10.5802/ambp.388/

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