Thread: Character Theory

Urgent answer required for these questions please!

(1) Show that if p(x) is a character of a group G then so is also 1/2{(p(x))^2 - p(x^2)}

(2) Let G be a finite group, A is a normal subgroup of G; suppose that for all a in A' = (A \ {1}), A = C_g (a) and that G\A is abelian.
Show that G has exactly (|A|-1)/|G:A| irreducible characters of degree greater than or equal to 2, which have degree |G:A|

Originally Posted by Turloughmack

Urgent answer required for these questions please!

(1) Show that if p(x) is a character of a group G then so is also 1/2{(p(x))^2 - p(x^2)}

Check Fulton and Harris this the natural representation on the exterior algebra (that is if is the representation came from).

(2) Let G be a finite group, A is a normal subgroup of G; suppose that for all a in A' = (A \ {1}), A = C_g (a) and that G\A is abelian.
Show that G has exactly (|A|-1)/|G:A| irreducible characters of degree greater than or equal to 2, which have degree |G:A|

You have yet to show any effort friend, come on.