Let $ \alpha = (1432)(257)(654) $.(a) Find a disjoint cycle decomposition of $ \alpha $, i.e. write $ \alpha $ as a product of disjoint cycles.(b) Find a transposition decomposition of $ \alpha $, i.e. write $ \alpha $ as a product of transpositions.(c) What is the order of $ \alpha $?(d) Is $ \alpha $ an even or odd permutation?

Given a permutation, α=1432257654 That is,…

Let a = (1432)(257)(654). (a) Find a disjoint cycle decomposition of a, i.e. write a as a product of disjoint cycles. (b) Find a transposition decomposition of a, i.e. write a as a product of transpositions. (c) What is the order of a? (d) Is a an even or odd permutation?

Let a = (1432)(257)(654). (a) Find a disjoint cycle decomposition of a, i.e. write a as a product of disjoint cycles. (b) Find a transposition decomposition of a, i.e. write a as a product of transpositions. (c) What is the order of a? (d) Is a an even or odd permutation?

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Power Operation

Power operation is topic of algebra in Math. It is use to represent repeated multiplication. Very big number and very small number can be easily express using power operation. Power operation is useful in many fields. In space engineering, it helps in representing the distance or size of particular heavenly body. In medical field, it is used to represent very small size. In medical field it helps to mention size of bacteria or virus.

Exponents

The exponent or power or index of a variable/number is the number of times that variable/number is multiplied by itself.

Question

Let $ \alpha = (1432)(257)(654) $.

(a) Find a disjoint cycle decomposition of $ \alpha $, i.e. write $ \alpha $ as a product of disjoint cycles.

(b) Find a transposition decomposition of $ \alpha $, i.e. write $ \alpha $ as a product of transpositions.

(c) What is the order of $ \alpha $?

(d) Is $ \alpha $ an even or odd permutation?

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