Exercise 6.5. Let G be a group and let S := {abab | a, b G}. The commutator subgroup ofG is the subgroup C generated by S, i.e.C =Ɑ H.(1) Show that C is a normal subgroup of G.H:H

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Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter4: More On Groups

Section4.5: Normal Subgroups

Problem 20E

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Let be a group of order 24. If is a subgroup of , what are all the possible orders of ?
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Exercise 6.5. Let G be a group and let S := {abab | a, b G}. The commutator subgroup of G is the subgroup C generated by S, i.e. C = Ɑ H. (1) Show that C is a normal subgroup of G. H:H