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4.60 (1973)

Solved

(P. Hall). What is the cardinality of the set of simple groups generated by two elements, one of order 2 and the other of order 3?

Contributor: D. M. Smirnov

Progress

The cardinality of the continuum. Every 2-generated group $G$ is embeddable into a simple group $H$ with two generators of orders 2 and 3 (P. E. Schupp, J. London Math. Soc., 13 (1976), 90–94). Such a group $H$ has at most countably many 2-generator subgroups, while there are continuum of groups $G$. (Yu. I. Merzlyakov, 1976.)

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