The almost simple groups invariably generated by an element of order 2 and an element of order 3 are exactly PGL2(3^{2^b}) for b ≥ 1.
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The structure of finite groups invariably generated by two elements of prime order
The almost simple groups invariably generated by an element of order 2 and an element of order 3 are exactly PGL2(3^{2^b}) for b ≥ 1.