ALMOST IDENTITIES IN GROUPS

Grigor G. Gevorkyan; Vachagan G. Dilanyan

doi:10.46991/PYSU:A.2024.58.1.008

Authors

Grigor G. Gevorkyan Chair of Algebra and Geometry, YSU, Armenia
Vachagan G. Dilanyan Chair of Algebra and Geometry, YSU, Armenia https://orcid.org/0009-0002-5933-8463

DOI:

https://doi.org/10.46991/PYSU:A.2024.58.1.008

Keywords:

n-periodic product, identity, probability, Cayley graph

Abstract

In this work we construct a group G, which generates the variety of all groups. At the same time, in each ball of the Cayley graph of this group G, the ratio of the number of elements that satisfy a fixed equation of the form $x^n=1$ to the number of all elements of this ball tends to one when the radius of the ball tends to $\infty$ .

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