Suppose that (G, *) is a group, with identity e, where cardinality of G is even. Show that there must be an element g in G, with g not equal to e and g*g=e.
Suppose that (G, *) is a group, with identity e, where cardinality of G is even. Show that there must be an element g in G, with g not equal to e and g*g=e.
If then . In other words the elements which aren't idempotent come in pairs.