Please solve all parts as soon as possible (a) Consider the symmetric group Sx on the set X = R-{0, 1}. Let f be the function defined by the followingrulex - 1f(r) =%3Dfor all r E X. Show that f E Sx, and find the order of f and the inverse of f.(b) Let G be a group of order 72. Show that if G is not cyclic, then for any g EG either g24 = 1 or g36 = 1.(c) Let G be a group of order 60 and g be an element of G of order 10. Show that there is no element r ofG satisfying r = g.

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Answered: (a) Consider the symmetric group Sx on…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.2: Properties Of Group Elements

Problem 23E: 23. Let be a group that has even order. Prove that there exists at least one element such that and...

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