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Questions about the branch of algebra that deals with groups.

15 votes
1 answer
685 views

Probability that a random element of a group is trivial

Let $G$ be an infinite group with a finite generating set $S$. For $n \geq 1$, let $p_n$ be the probability that a random word in $S \cup S^{-1}$ of length at most $n$ represents the identity. Is it …
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