Random Burnside Groups
O. Kharlampovich, A. Myasnikov

TL;DR
This paper proves that for sufficiently large odd exponents, random groups are almost surely infinite, extending understanding of group properties in probabilistic models.
Contribution
It establishes the infiniteness of random groups with large odd exponents in both the few relator and density models, a new result in probabilistic group theory.
Findings
Random groups of large odd exponent are infinite with high probability.
The result applies to both the few relator and density models.
Provides new insights into the structure of random Burnside groups.
Abstract
We show that there exists a positive number such that for any odd a random group of exponent with overwhelming probability is infinite in the few relator model and in the density model for small .
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Taxonomy
TopicsTopological and Geometric Data Analysis · Geometric and Algebraic Topology · Advanced Topology and Set Theory
