f = (7 3)(14 85 37 6) g = (5 8 26143) Write each of the following permutations as a product of disjoint cycles, separated by commas (e.g. (1,2), (3, 4, 5), ... ). Do not include 1-cycles (e.g. (2) ) in your answer. (a) fg = (b) ƒ-1 (c) fgƒ¬l = Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x) so (1, 3)(1, 2) = (1, 2, 3) not (1, 3, 2).

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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 Let f and g be permutations on the set {1,2,3,4,5,6,7,8}{1,2,3,4,5,6,7,8}, defined as follows

 

 

f = (7 3)(148537 6)
g = (5 8 26143)
Write each of the following permutations as a product of disjoint cycles, separated by commas (e.g. (1,2), (3,4, 5), ... ).
Do not include 1-cycles (e.g. (2) ) in your answer.
(a) fg =
(b) ƒ-l =
(c) fgƒ-l =
Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x) so (1, 3)(1, 2) = (1,2,3) not (1, 3,2).
Transcribed Image Text:f = (7 3)(148537 6) g = (5 8 26143) Write each of the following permutations as a product of disjoint cycles, separated by commas (e.g. (1,2), (3,4, 5), ... ). Do not include 1-cycles (e.g. (2) ) in your answer. (a) fg = (b) ƒ-l = (c) fgƒ-l = Assume multiplication of permutations f,g obeys the rule (fg)(x) = f(g(x) so (1, 3)(1, 2) = (1,2,3) not (1, 3,2).
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