1. Given the set A = {1,2,3,4,5,6}. Given S6 = {f: A→ Alf bijective mapping} is a group with respect to the function composition operation A. Is there any f € So that satisfies o (f) = 4? B. Is there any f E So that satisfies o (f) = 7? 1 2 3 4 5 6 C. If f = 6), define f2022 3 4 5 2 1 6.

1. Given the set A = {1,2,3,4,5,6}. Given S6 = {f: A→ Alf bijective mapping} is a group with respect to the function composition operation A. Is there any f € So that satisfies o (f) = 4? B. Is there any f E So that satisfies o (f) = 7? 1 2 3 4 5 6 C. If f = 6), define f2022 3 4 5 2 1 6.

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 26E: 26. Suppose is a finite set with distinct elements given by . Assume that is closed under an...

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Question

Please solve the problem abstract algebra subparts a,b,c max in 30-45 minutes thank u

1. Given the set A = {1,2,3,4,5,6}.
Given
S6 = {f: A→ Alf bijective mapping} is a group with respect to the
function composition operation
A. Is there any f € So that satisfies o(f) = 4?
B. Is there any f E So that satisfies o (f) = 7?
1
2 3 4 5
C. If f
6), define f2022
3
4 5 2
=
1 6.

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