Connected triple supports generate an alternating group
= Connected triple supports generate an alternating group
A connected finite hypergraph of three-element supports, with a <three-cycle> on each support, generates the full alternating group. To merge a new triple meeting an old alternating support in two letters, conjugate over unordered pairs of old letters. For one-letter overlap compare $(a\,b\,c)$ and $(a'\,b\,c)$: their quotient is $(a\,b\,a')$, reducing to two two-letter-overlap steps.