bb1.Advance maths. (4) Let G = {e, a, a², a³, aª, a5} be a cyclic group of order 6.(a) Construct the subgroup of G generated by the element a².(b) What are the possible orders of subgroups of the group G?(c) Find all subgroups of the group G.

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Answered: (4) Let G = {e, a, a², a³, aª, a5} be a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.7: Direct Sums (optional)

Problem 12E

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(4) Let G = {e, a, a², a³, aª, a5} be a cyclic group of order 6. (a) Construct the subgroup of G generated by the element a². (b) What are the possible orders of subgroups of the group G? (c) Find all subgroups of the group G.