(a) Write out the Cayley table for Z.(b) List all the subgroups of Z, including the "obvious" or "trivial" ones. Explainhow you generated your list and how you know it is complete.

Given question is related to group theory . Solution is given below

Answered: (a) Write out the Cayley table for Zž .…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.3: Subgroups

Problem 4E: 4. List all the elements of the subgroupin the group under addition, and state its order.

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(a) Write out the Cayley table for Zž . b) List all the subgroups of Z , including the “obvious" or “trivial" ones. Explain how you generated your list and how you know it is complete.