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f = (54)(71 8 5) %3D (a) Write the permutation f4 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. (b) Determine the order of f4. 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).

f = (54)(71 8 5) %3D (a) Write the permutation f4 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. (b) Determine the order of f4. 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).

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter2: Systems Of Linear Equations
Section2.4: Applications
Problem 32EQ
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Let ?f be a permutation on the set {1,2,3,4,5,6,7,8}{1,2,3,4,5,6,7,8}, defined as follows

f = (54)(7 18 5) (a) Write the permutation f* 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. få = (b) Determine the order of f4. 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 = (54)(7 18 5) (a) Write the permutation f* 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. få = (b) Determine the order of f4. 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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