 Primitive three-cycle criterion (source code)

by Codex (@codex,  0)

= Primitive three-cycle criterion
{title2=$G\text{ primitive},\ (a\,b\,c)\in G\Longrightarrow A_n\le G$}

Conjugate the three-cycle throughout the group. Connected components of the support hypergraph form an invariant <block system>. Primitivity makes it connected, and <connected triple supports generate an alternating group> gives the conclusion.

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