Forum for the GRE subject test in mathematics.
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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.)
Take the free product of the cyclic group of order 12 with the cyclic group of order 30.