Is there an infinite group that has finite subgroup with finite index?
I can find one, if the index is infinite - but what if the index is finite?
Thanks
2026-03-27 03:43:15.1774582995
Is there an infinite group that has finite subgroup with finite index?
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No. If $H$ is a finite subgroup of finite index in a group $G$, then $\left| G\right| = \left| H\right|[G:H]$ is finite.