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512 p. Introduction to abstract algebra. New York, New York, 303 p. van der Waerden, B. L. 1949. 264 p. London, 563 p. MacDuffee, C. C. S. 2d ed. Theory and application of infinite series. Hafner, 1951. Wiley, Berlin, Springer-Verlag, Modern algebra. Vol. 1.
PROOF. 50. < b- PROOF. 2-1 (b) . j,0 (-1)ib-1 2 ' if lb) > 1. 2). 2 is absolutely convergent and alternating, the theorem follows by grouping the terms in pairs. 1 SOME APPLICATIONS Generalized elementary Abelian groups. In this and the following two sections we shall collect the applications indicated above, establish some new ones, and make conjectures regarding others. 6 we noted that when b is a prime N(b) is the number of subgroups of order bg in an elementary Abelian group of order bk. 3 which established that 2(b) represents the number of subgroups in an elementary Abelian group of order bk when b is a prime.
1) we will consider two cases: (1) 0 < g