Latin Squares and Finite Groups
January 24, 2018
Last semester, for an algebra homework, I was trying to prove that there exist only 2 groups of order 6 (namely \(\mathbb{Z}_6\) and \(S_3\) ). The usual argument uses the classification of groups with order \(pq\) (with \(p\) and \(q\) prime), which itself uses Sylow theorems, but I wondered if I could prove it computationally. Here’s my attempt. Definition: a magma is a pair \( (G,\ast) \) where \(G\) is a non-empty set and \(\ast\) is a binary operation on \(G\) . ...