# Abstract algebra homework problem

• Nov 30th 2008, 08:39 AM
jackiemoon
Abstract algebra homework problem
Hi,

I need some urgent help with this one please:

Let G be the set {a,b,c}.
Construct the Cayley table for all possible operations on g such that G with each of the defined operations is a group with b as identity. How many such operation exist? Are any of the resulting groups non-Abelian?

Any tips/advice would be much appreciated.

Regards
• Nov 30th 2008, 09:52 AM
TheEmptySet
Quote:

Originally Posted by jackiemoon
Hi,

I need some urgent help with this one please:

Let G be the set {a,b,c}.
Construct the Cayley table for all possible operations on g such that G with each of the defined operations is a group with b as identity. How many such operation exist? Are any of the resulting groups non-Abelian?

Any tips/advice would be much appreciated.

Regards

See the attached immage

Attachment 9003

To be a group each element must appear exactly once in each row and column. How many different ways can you do this.

I hope this helps. Good luck.