Let S be a set with an associative binary operation but with no identity. Choose an element 1 not belonging to S, write M = {1} or S, and define an operation on M by using the operation of S and 1s=s=s1 for all s belonging to S. Show that M is a monoid.
Show that $ and %$%^-1 have the same parity for all % and $ in Sn. (Sn is the symmetric group of degree n)
Permutations : Disjoint Transpositions
If $ belongs to Sn (where Sn is the symmetric group of degree n), show that $^2 = % if and only if $ is a product of disjoint transpositions.
Define the sign of a permutation $ to be: sgn $ = 1 if $ is even. -1 if $ is odd. Prove that sgn($%) = sgn$sgn% for all $ and % in Sn.
Please if you are going to solve this problem please be very accurate!! (and careful!!). I have used brainmass before and have recieved incorrect answers on mulitple occations (answers that initially seemed correct) and it has hindered my studying. I have decided to give it another chance. With that said, thank you very much for ...continues
Please if you are going to solve this problem please be very accurate!! (and careful!!). I have used brainmass before and have recieved incorrect answers on mulitple occations (answers that initially seemed correct) and it has hindered my studying. I have decided to give it another chance. With that said, thank you very much for ...continues
Please if you are going to solve this problem please be very accurate!! (and careful!!). I have used brainmass before and have recieved incorrect answers on mulitple occations (answers that initially seemed correct) and it has hindered my studying. I have decided to give it another chance. With that said, thank you very much for ...continues
Please if you are going to solve this problem please be very accurate!! (and careful!!). I have used brainmass before and have recieved incorrect answers on mulitple occations (answers that initially seemed correct) and it has hindered my studying. I have decided to give it another chance. With that said, thank you very much for ...continues
Please if you are going to solve this problem please be very accurate!! (and careful!!). I have used brainmass before and have recieved incorrect answers on mulitple occations (answers that initially seemed correct) and it has hindered my studying. I have decided to give it another chance. With that said, thank you very much for ...continues
Please if you are going to solve this problem please be very accurate!! (and careful!!). I have used brainmass before and have recieved incorrect answers on mulitple occations (answers that initially seemed correct) and it has hindered my studying. I have decided to give it another chance. With that said, thank you very much for ...continues
