Holiday quiz I- groups

Which one of the properties is known as Associative property?

• a+b =b+a

• a+(b+c) = (a+b) +c

• a*b=b*a

• a*e=e*a =a

In N we define a*b=a. Then (N,*) is

• Group

• Abelian group

• Not group

If (a,b)*(c,d)=(ab,bc+d), then identity element is

• (0,0)

• (1,1)

• (0,1)

• (1,0)

The number of elements in the symmetric group s_n is

• n

• 2n

• n!

• n²

Say true or false:Any permutation can be expressed as a product of transpositions.

• True

• False