Suppose $G$ is a cyclic group $C_{5} <S_{5}$. Does anybody know what the torsion-free part of the centralizer of this group is?
2025-01-14 12:00:50.1736856050
Free torsion part of centralizer of a cyclic group
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Each nontrivial torsion-free group is infinite; contrapositively, each finite group has torsion. Thus there is no torsion-free part as $\lvert S_5\rvert<\infty$.