This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: ...one, it would have three elements in common with v. This would lead either to to the type A) or to the rejected first case of 117. If the new substitutions contained only one of the new elements xi, x3, x5, xe and three new ones, then we should have the fifth case of 117, and this is also to be rejected. There remains ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1892 Excerpt: ...one, it would have three elements in common with v. This would lead either to to the type A) or to the rejected first case of 117. If the new substitutions contained only one of the new elements xi, x3, x5, xe and three new ones, then we should have the fifth case of 117, and this is also to be rejected. There remains only the case where the new substitution connects two of the elements x, x2, x5, xe, with two others. It must then be of one of the forms XXf) (X2Xi, )) XXa) yXjXb)) yXiXa) yXXf) (x2xa) (x5x5), (x2x ) (xx), Xz, xa) yXfpCj, Of these the first, third, fourth and sixth stand in the relation defined by C) to r, while the first, second, fifth and sixth stand in the same relation to v. All the groups B) therefore occur under i either A) or C), and we may pass at once to the last case. 120. C). In this case the required group contains ti = (a?, U?2) (-3a;4) a2---X) (x3X6), a3--t-ir2a, = (x2x5) (x4x6). "We consider first the case n = 6. The elements xi, x2, xs are not yet connected with x3, xi, xa. There must be a connecting substitution in the group of the type (xaXp) (xyxs), where we may assume that xa is "contained among the the three elements xi, x2, x5. If xa were x2 or x5, then we should obtain, by transformation with respect to r, or r2, a substitution (xix) (xjcf, so that we may assume a = 1. The possible cases are then (a) (xiOJ2) (xsxm), (x, x5) (x2xm), (x2x5) (#, #, ) m = 3,4,6. (/3) (xiXm) (x xp), m, n, p = 3,4,6. (r) (xix ) (x2x ), (xixm) (x5x ), m, n = 3,4,6. The substitutions of the first and second lines are to be rejected, since their products with ru a2, t3 lead to the first case in 117, or directly to substitutions wtth only three elements. There remain, for the di...
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Add this copy of The Theory of Substitutions and its Application to to cart. $32.92, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
Add this copy of The Theory of Substitutions and its Application to to cart. $42.59, new condition, Sold by Ria Christie Books rated 5.0 out of 5 stars, ships from Uxbridge, MIDDLESEX, UNITED KINGDOM, published 2022 by Legare Street Press.
