Largeness and equational probability in groups
Abstract
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 Gn is already the whole of Gn , 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.
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