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
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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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