Israel Journal of Mathematics· 2026Q1
Probabilistic laws on infinite groups
- 3citations
- Q1SCImago
- 2026year
Short summary
Infinite groups can satisfy certain laws (like metabelian) with high probability via random walks, even if they don't satisfy the law virtually.
AI-generated from the title and abstract; the full text is not read.
Key points
- Constructed infinite groups satisfying metabelian law with high probability via random walks.
- These groups do not satisfy the metabelian law virtually.
- Proved that any infinite group satisfying x^2 = 1 with positive probability is virtually abelian.
AI-generated from the title and abstract; the full text is not read.
Abstract
Abstract We study the probability that certain laws are satisfied on infinite groups, focusing on elements sampled by random walks. For several group laws, including the metabelian one, we construct examples of infinite groups for which the law holds with high probability, but the group does not satisfy the law virtually. On the other hand, we show that if an infinite group satisfies the law x 2 = 1 with positive probability, then it is virtually abelian.
The authors' abstract, as published at the source. Israel Journal of Mathematics, 2026 · DOI ↗
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Field: Discrete Mathematics and Combinatorics
Discrete Mathematics and CombinatoricsMathematics