(Countably) infinite group generated by finite subgroups.

Forum for the GRE subject test in mathematics.
doryphorus
Posts: 5
Joined: Mon Oct 05, 2015 2:23 am

(Countably) infinite group generated by finite subgroups.

Postby doryphorus » Mon Oct 19, 2015 11:38 am

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.)

grad
Posts: 31
Joined: Sun Nov 09, 2014 1:02 am

Re: (Countably) infinite group generated by finite subgroups.

Postby grad » Fri Nov 27, 2015 10:13 am

Take the free product of the cyclic group of order 12 with the cyclic group of order 30.




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