= Tarski monster groups are two-generated and simple
{c}
For a <Tarski monster group>, any nonidentity element generates a proper subgroup of order $p$. Adjoining an element outside that subgroup generates the whole group. A proper nontrivial normal subgroup would have order $p$; conjugation into its finite automorphism group forces it to be central. Combining it with another order-$p$ cyclic subgroup would then give a proper subgroup of order $p^2$, a contradiction.
// Target: algebra.bigb
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