Primitive permutation group (original) (raw)

In mathematics, a permutation group G acting on a non-empty finite set X is called primitive if G acts transitively on X and the only partitions the G-action preserves are the trivial partitions into either a single set or into |X| singleton sets. Otherwise, if G is transitive and G does preserve a nontrivial partition, G is called imprimitive. This terminology was introduced by Évariste Galois in his last letter, in which he used the French term équation primitive for an equation whose Galois group is primitive.