3.a) In G = (Z54,) find [G:H] for H=< 24 >.b) Let |G|=8 and G is not cyclic. Show that g4= e for every gEG.

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Answered: a) In G = (Z54,) find [G:H] for H=< 24…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 30E: Exercises 30. For an arbitrary positive integer, prove that any two cyclic groups of order are...

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a) In G = (Z54,) find [G:H] for H=< 24 >. b) Let |G|=8 and G is not cyclic. Show that g4 = e for every g E G.