# Answer to Question #44728 in Abstract Algebra for jasvinder

Question #44728

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).

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).

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