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(3) Let G be a finite group and let element a in Aut(G) be an automorphism og G. Let X be an element of Irr(G) be an irreducible character of G.
Define (X)^a(g) := X(g^a). Is (X)^a irreducible?
Urgent answer required for these questions please!
(3) Let G be a finite group and let element a in Aut(G) be an automorphism og G. Let X be an element of Irr(G) be an irreducible character of G.
Define (X)^a(g) := X(g^a). Is (X)^a irreducible?
Think back to what irreducible characters are--they are the characters of irreps onOriginally Posted by Turloughmack
. So, let
and let
be the irrep it came from. Then, as you can easily verify
as you denoted is the character of
(which is a representation since
). Now, if
left any non-trivial proper subspace of
is bijective) that same subspace would be
-invariant? So...
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