Answer to Question #44728 in Abstract Algebra for jasvinder

Question

a) Let D(subscript2n) = (x,y|x^2 = e, y^n = e, xy = xy^(−1) i
Prove the relation
x^iy^jx^ky^l =( x^iy^(j+l) if k is even
( x^(i+k)y^(l−j) if k is odd.
Further, find all the elements of order 2 in D(subscript12).

b) Find two different Sylow 2-subgroups of D(subscript12).