What is an example of an infinite group with a composition series and infinitely many simple subgroups?
Example of infinite group with infinitely many simple subgroups
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abstract-algebra
finite-groups
1 Answers
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One example is the direct sum of all the finite simple groups (more precisely, pick one for each isomorphism class).
Another (perhaps less cheat-y) one is the group of permutations of $\mathbb N$, which contains all the alternating groups $A_n$ as subgroups.
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0I see - I think the part I was missing was that $A_{\text{finitary}}$ is also simple. – 2012-11-12