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f 7 / = l — 11 + 9 + 1 1 — 9 — 11 + 9 + 1 1 Since UTJ' = 0, we have U • U' = 0. As all the terms in U are of the same sign, it is easily seen that U is divergent for all positive integral values of p. XV and U' are also divergent. § 8. If we assume t = 2, s — 1, c = — 1, a0 = 1, 60 = 1, iV== 0, then the condition that the sum of the product of (5) and (6) shall vanish becomes d + 1 = 0 and (letting i = j / —• 1) the factor series thus obtained are the two complex divergent series 1 + (1 + i) + i + 0 + 1 + (i + 1) + i + 0 + • • •

Three sets of generational relations defining the abstract simple group of order 504