I am looking for a concrete example of an infinite simple group with two generators. Ideally, one generator has order 2, the other 3, but if there is a nice example without this requirement, it will be appreciated. Schupp proved that every countable group embeds into such a group, but I would like to see a concrete easy example (where it is easy to show simplicity).
Infinite 2-generated simple group
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group-theory
simple-groups