MODERN ALGEBRA I

Assignment IV

Miliyon Tilahun (NSR/4137/05)

September 8, 2015

Let A = {1,2,3,4,5,6}

S6 = { f | f : {1,2,3,4,5,6} {1,2,3,4,5,6} and f is 11 and onto}

Let =(1 2 3 4 5 63 4 5 1 6 2

)and =

(1 2 3 4 5 63 4 2 5 6 1

)Find(i). (ii). (iii). 2 (iv).1

Solution: = (135624) and = (132456)i.

(135624) (132456)= (152)(346)= (152)(346). i.e. =

(1 2 3 4 5 65 1 4 6 2 3

)ii.

(132456) (135624)= (125)(364)= (125)(364). i.e. =

(1 2 3 4 5 62 5 6 3 1 4

)iii. 2 =

(132456) (132456)= (125)(346) = 2 = (125)(346). i.e. 2 =

(1 2 3 4 5 62 5 4 6 1 3

)iv. 1

(132456)1 = (165423)i.e. 1 =

(1 2 3 4 5 66 3 1 2 4 5

)

1