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(Countably) infinite group generated by finite subgroups.

Posted: Mon Oct 19, 2015 11:38 am
by doryphorus
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.

Posted: Fri Nov 27, 2015 10:13 am
by grad
Take the free product of the cyclic group of order 12 with the cyclic group of order 30.