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Jun 7, 2023 at 5:21 comment added M.Ramana Sorry, I forgot to say that that I'm looking for groups with finitely many retracts other simple groups because they are trivial examples with just two retracts. Even more, splitting-simple groups have only two retracts like $\mathbb{Z}$ and every simple group is splitting-simple. By a splitting-simple group, I mean a group which has no proper nontrivial retracts.
Jun 6, 2023 at 16:54 history answered Jeremy Rickard CC BY-SA 4.0