Question

Given that aa and bb belong to an Abelian group and that |a|=6|a|=6 and |b|=6|b|=6, what can you say about |ab||ab|?

My solution

|a|=6a=6a6=e

|a|=6 \\

a=6 \\

a^6=e

similarly:

|b|=6b=6b6=e

|b|=6 \\

b=6 \\

b^6=e

hence

|ab|=(ab)(ab)=(ab)6=a6b6=ee=e

|ab|=(ab) \\

(ab)=(ab)^6=a^6b^6=ee=e

therefore, |ab|=6|ab|=6, and abab belongs to GG.

Q: Pls what sis I do wrong in answering the question???

Thanks

=================

=================

2 Answers

2

=================

Saying that |a|=6|a|=6 means that a6=ea^6=e and ak≠ea^k\ne e, for 0