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Math Help - Character Theory

  1. #1
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    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|
    Last edited by Ackbeet; May 11th 2011 at 02:01 PM. Reason: Splitting threads.
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by Turloughmack View Post
    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 {\bigwedge}{}^2(V) (that is if \rho:G\to\text{GL}(V) is the representation \chi 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.
    Last edited by Drexel28; May 11th 2011 at 07:21 PM.
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