(Countably) infinite group generated by finite subgroups.

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 Joined: Mon Oct 05, 2015 2:23 am
(Countably) infinite group generated by finite subgroups.
Could someone please give me an example of an infinite group generated by two finite subgroups? (I think you know the question I'm referring to, if a subgroup H has order 12 and K has order 30 what could be the order of the subgroup generated by H and K.)
Re: (Countably) infinite group generated by finite subgroups.
Take the free product of the cyclic group of order 12 with the cyclic group of order 30.