DETERMINATION OF ALL THE GROUPS OF ORDER jT, p BEING ANY PRIME, WHICH CONTAIN THE ABELIAN GROUP OF ORDER pTM- AND OF TYPE

we shall have the definition given by H. Weber, loo. cit. That these postulates 1, 2, 3', 4', 5a are mutually independent (when n > 2) has already been shown in the writer's previous paper (page 300). I t should be noticed, however, that postulates 1, 2, 3', 4', 56 would not be sufficient to define an infinite group, since the system of positive integers, with a o b = a + 6, satisfies them all, and is not a group.