final year project topics and materials

Abstract
Let X { n} n = 1,2,…, be a finite n -element set and let n n n S , A and D be the
Symmetric, Alternating and Dihedral groups of n X , respectively. In this thesis we
obtained and discussed formulae for the number of even and odd permutations (of an
n − element set) having exactly k fixed points in the alternating group and the
generating functions for the fixed points. Further, we give two different proofs of the
number of even and odd permutations (of an n − element set) having exactly k fixed
points in the dihedral group, one geometric and the other algebraic. In the algebraic
proof, we further obtain the formulae for determining the fixed points. We finally
proved the three families; F(2r,4r + 2), F(4r +3,8r + 8) and F(4r +5,8r +12) of the
Fibonacci groups F(m , n) to be infinite by defining Morphism between Dihedral
groups and the Fibonacci groups