11.5.5. Let G = (Z/24Z, +).(a) Find a subgroup H of G that is isomorphic to (Z/4Z, +). How manychoices for such an H are there?(b) Find a familiar group that is isomorphic to G/H.(c) Find a subgroup K of G/H of order 3.(d) Find a familiar group that is isomorphic to (G/H)/K.

(a) Subgroup H={0,6,12,18} is isomorphic to (Z/4Z,+), with one choice.(b) G/H is isomorphic to…

Answered: 11.5.5. Let G = (Z/24Z, +). (a) Find a…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 28E

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11.5.5. Let G = (Z/24Z, +). (a) Find a subgroup H of G that is isomorphic to (Z/4Z, +). How many choices for such an H are there? (b) Find a familiar group that is isomorphic to G/H. (c) Find a subgroup K of G/H of order 3. (d) Find a familiar group that is isomorphic to (G/H)/K.