ALMOST IDENTITIES IN GROUPS - Gevorkyan, Grigor G.; Dilanyan, Vachagan G. (Proceedings of the YSU A: Physical and Mathematical Sciences, 2024)
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 $∞$ .
Keywords: n-periodic product; identity, probability; Cayley graph