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If an n-cycle o e S, is a product of an even number of transpositions then o is called an even permutation otherwise it is called an odd permutation. State whether the following permutations are odd or even. (a) (13 2 4) € S4. (b) (1 4 3)(2 5 6 7) E S7. (c) (143 6)(2 9 57 8) € S9.

If an n-cycle o e S, is a product of an even number of transpositions then o is called an even permutation otherwise it is called an odd permutation. State whether the following permutations are odd or even. (a) (13 2 4) € S4. (b) (1 4 3)(2 5 6 7) E S7. (c) (143 6)(2 9 57 8) € S9.

Algebra: Structure And Method, Book 1
Algebra: Structure And Method, Book 1
(REV)00th Edition
ISBN:9780395977224
Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Publisher:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. Cole
Chapter6: Fractions
Section6.4: Least Common Denominators
Problem 45WE
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If an n-cycle o e S, is a product of an even number of transpositions then o is called an even permutation otherwise it is called an odd permutation. State whether the following permutations are odd or even. (a) (132 4) € S4. (b) (1 4 3)(2 5 6 7) e S7. (c) (1 4 3 6)(2 9 57 8) E S9. (1 2 3 4 5 6 7 8 9 (d) 2 4 5 1 3 7 89 6 S9
Transcribed Image Text:If an n-cycle o e S, is a product of an even number of transpositions then o is called an even permutation otherwise it is called an odd permutation. State whether the following permutations are odd or even. (a) (132 4) € S4. (b) (1 4 3)(2 5 6 7) e S7. (c) (1 4 3 6)(2 9 57 8) E S9. (1 2 3 4 5 6 7 8 9 (d) 2 4 5 1 3 7 89 6 S9
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