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Theory of groups of finite order. Cambridge, 1911. Knopp, K. 1940. 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.

1) for h O. 2. 7 yields Let b have period p. Then (1+x)101--, and (1+x)(b) does not exist for any other x when pX 1 when lx1 <1, 1. The above theorem reveals that the exponent 1-p behaves like the 26 exponent zero when b has period p and Ixf <1. 1. 3. If b has period p, (1+x) (b) = (1+x) and only if lx1 <1. 4. If b has period p, the following laws of exponents hold if and only if ixi and lyj are both less than one. 4) PROOF. (14-xra(14y)7. 3. 3 and elementary algebra. 3. 1t The two theorems of this section completely characterize 1t(b).

PROOF. 1) we will consider two cases: (1) 0 < g

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