Geodesic
Almost identities in groups
Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 58 (2024) no. 1, pp. 8-12

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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 $\infty$ .
Keywords: $n$-periodic product, identity, probability, Cayley graph 
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G. G. Gevorgyan; V. G. Dilanyan. Almost identities in groups. Proceedings of the Yerevan State University. Physical and mathematical sciences, Tome 58 (2024) no. 1, pp. 8-12. http://geodesic.mathdoc.fr/item/UZERU_2024_58_1_a1/