ABSTRACT
Generation of a non-Abelian group is often much more subtle than gen eration of an Abelian group; although |Sn| = n!, which grows rapidly as n increases, Sn is generated by two elements having respective orders 2 and n, cf. Exercise 5.8 . Nevertheless, the non-Abelian groups G of immediate interest to us will be described explicitly in terms of two generators a, 6 such that G = (a)(5), z.e., G = {αι& : 0 < i < u, 0 < j < u} for suitable u,v (which is impossible for Sn, n > 6, cf. Exercise 11). Also these groups will be defined by rather few relations.
