Dear GAP Forum,
I hope you will excuse me for posting the following non-GAP-related question:
Let G be a finite group and let V be a complex finite dimensional
representation of G with character \chi.
Let Ker(\chi) = {g \in G | \chi(g) = deg(\chi)} and let
|Ker(\chi)| = {g \in G | |\chi(g)| = deg(\chi)}.
It is well know that the above two sets are equal to the sets
{g \in G | g acts as identity on V},
{g \in G | g acts by a scalar on V}, respectively.
Now let H be a normal subgroup of G.
Then the set of irreducible character \chi of G such that H < Ker(\chi)
is in one-to-one correspondence with irreducible characters of the
quotient group G/H.
My question is: what can be said about the set of irreducible characters
\chi of G such that H < |Ker(\chi)|?
What is H is abelian?
Best regards,
D. Naidu
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