Probabilistic Laws on Infinite Groups

Gideon Amir; Guy Blachar; Maria Gerasimova; Gady Kozma

Probabilistic Laws on Infinite Groups

Gideon Amir, Guy Blachar, Maria Gerasimova, Gady Kozma

Department of Mathematics

Research output: Working paper / Preprint › Preprint

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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.

Original language	English
Publisher	arXiv preprint
State	Published - 18 Apr 2023

Bibliographical note

39 pages,1 figure

Keywords

math.GR
math.PR
20P05, 20F69, 20F65, 60B15, 20E22

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2304.09144v1

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title = "Probabilistic Laws on Infinite Groups",

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AU - Blachar, Guy

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Y1 - 2023/4/18

N2 - 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.

AB - 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.

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KW - math.PR

KW - 20P05, 20F69, 20F65, 60B15, 20E22

M3 - פרסום מוקדם

BT - Probabilistic Laws on Infinite Groups

PB - arXiv preprint

ER -

Probabilistic Laws on Infinite Groups

Abstract

Bibliographical note

Keywords

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Cite this