FOLLOW THE INSTRUCTIONS AND ANSWER COMPLETELY AND TYPEWRITTEN FOR UPVOTE.NOT FOLLOWING MY INSTRUCTIONS GETS DOWNVOTE (a) Write the Cayley table for the group U(15).(b) Give an example of an infinite group and elements a, b G for which a¹bab.Define the operation o on the set R* x R = {(a, b) | a, b = R, a # 0} by (a, b) o (c,d) = (ac, be+d).Prove that (R* x R, o) forms a group.

U(15) is the set of all elements in ℤ15={0,1,2,3,4,5,6,7,8,9,10,11,12,13,14} ; x≡x ,such that…

Answered: -) Write the Cayley table for the group…

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-) Write the Cayley table for the group U(15).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter3: Groups

Section3.5: Isomorphisms

Problem 8E: Exercises 8. Find an isomorphism from the group in Example of this section to the multiplicative...

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FOLLOW THE INSTRUCTIONS AND ANSWER COMPLETELY AND TYPEWRITTEN FOR UPVOTE.

NOT FOLLOWING MY INSTRUCTIONS GETS DOWNVOTE

(a) Write the Cayley table for the group U(15).
(b) Give an example of an infinite group and elements a, b G for which a¹bab.
Define the operation o on the set R* x R = {(a, b) | a, b = R, a # 0} by (a, b) o (c,d) = (ac, be+d).
Prove that (R* x R, o) forms a group.

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