= Torsion conjugacy bound for a Dehn presentation
{title2=$|w|\leq\lfloor|r|/2\rfloor$}
In a finite <Dehn presentation>, every nonidentity finite-order element has a <shortest conjugacy representative> of length at most half the length of some <relator>. Indeed a positive power contains a Dehn segment. If the representative had length at least $k=\lfloor|r|/2\rfloor+1$, the first $k$ letters of that segment would fit into a cyclic rotation and could be replaced by fewer letters, contradicting minimality. Bounded <relator> lengths and a finite alphabet therefore give finitely many <conjugacy classes> of finite-order elements. With no <relators> the group is free and torsion-free, so only the identity class remains.
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