I have a question in representation theory. There is a result that says that if I have a linear character of a subgroup H of a group G with kernel K, then the induced character is irreducible iff (H,K) is a Shoda pair.
The proof uses the fact that
If, chi(ghg-1)=chi(h) for all h in H ∩ g-1Hg, then
[H,g]∩H ⊂ K.
I am not able to prove this one...can sumbody help??
The proof uses the fact that
If, chi(ghg-1)=chi(h) for all h in H ∩ g-1Hg, then
[H,g]∩H ⊂ K.
I am not able to prove this one...can sumbody help??