In a Group S, ab!=ba, choose the possible relationship?

Forum for the GRE subject test in mathematics.
dumplinghao123
Posts: 24
Joined: Sat Sep 22, 2012 4:34 pm

In a Group S, ab!=ba, choose the possible relationship?

Postby dumplinghao123 » Sat Sep 22, 2012 4:35 pm

A. a^2=b^2
B.aba=1

vonLipwig
Posts: 51
Joined: Sat Mar 17, 2012 9:58 am

Re: In a Group S, ab!=ba, choose the possible relationship?

Postby vonLipwig » Sat Sep 22, 2012 11:20 pm

To investigate whether the first one is possible, think of some small groups and try and find a and b with a^2 = b^2 and ab =/= ba.

For the second, manipulate the equation aba = 1 and see what happens.

dumplinghao123
Posts: 24
Joined: Sat Sep 22, 2012 4:34 pm

Re: In a Group S, ab!=ba, choose the possible relationship?

Postby dumplinghao123 » Sat Sep 22, 2012 11:35 pm

Oh thanks! I see the second one now.

vonLipwig wrote:To investigate whether the first one is possible, think of some small groups and try and find a and b with a^2 = b^2 and ab =/= ba.

For the second, manipulate the equation aba = 1 and see what happens.

vonLipwig
Posts: 51
Joined: Sat Mar 17, 2012 9:58 am

Re: In a Group S, ab!=ba, choose the possible relationship?

Postby vonLipwig » Sun Sep 23, 2012 3:26 am

Excellent. What did you get?

For the first one, try the symmetric group S_3.

dumplinghao123
Posts: 24
Joined: Sat Sep 22, 2012 4:34 pm

Re: In a Group S, ab!=ba, choose the possible relationship?

Postby dumplinghao123 » Sun Sep 23, 2012 11:57 am

yes. Coz ab=ab(aba)=(aba)ba=ba if aba=1
and S3 is a brilliant idea! thanks!

vonLipwig
Posts: 51
Joined: Sat Mar 17, 2012 9:58 am

Re: In a Group S, ab!=ba, choose the possible relationship?

Postby vonLipwig » Sun Sep 23, 2012 12:10 pm

Yep! Good work =)




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