19. a. Show that Z15 is isomorphic to Z3 Zs, where the group operation in each of Z15,Z3, and Z5 is addition.b. Show that Z12 is isomorphic to Z3 Z4, where all group operations are addition.

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Answered: 19. a. Show that Z15 is isomorphic to…

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 19E: 19. a. Show that is isomorphic to , where the group operation in each of , and is addition. ...

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19. a. Show that Z15 is isomorphic to Z3 Zs, where the group operation in each of Z15, Z3, and Z5 is addition. b. Show that Z12 is isomorphic to Z3 Z4, where all group operations are addition.