can someone please help me with 3a and 3b c The product of a

can someone please help me with 3a and 3b?

(c) The product of an even permutation and an odd p 3 (a) A cycle of length is even if I is odd. is odd if I is even. (b) A cycle of length

Solution

3. a) & b)

For l = 2 i.e. even

a = (a1a2)

Thus, cycle is odd with 1=(2-1).

For l = 3 i.e. odd

a = (a1a3) (a1a2)

Thus, cycle is even with 2=(3-1).

For l=l+1,

a = (a1a(l+1)) (a1al) .... (a1a2)

Thus cycle is a product of l transportations.

Since, l+1 and l have opposite parity, for odd l, cycle of length l is even and for even l, cycle of length is odd.