As the question title suggests, for what integers $n$ is the group $S_n$ generated by an element of order $2$ together with an element of order $3$?
2026-04-01 22:49:44.1775083784
For what integers n is the group S_n generated by an element of order 2 together with an element of order 3?
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See http://www.math.uconn.edu/~kconrad/blurbs/grouptheory/genset.pdf, all values of $n$ except 2, 5, 6, 8. The result is old, going back to Miller in 1901.