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9 votes
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An identity for characters of the symmetric group

I am looking for a reference for the identity $$\chi_\lambda(C)=\frac{\dim(V_\lambda)}{|C|}\sum_{p\in P_\lambda,\,q\in Q_\lambda,\,pq\in C}\operatorname{sgn}(q)$$ for the irreducible characters of the ...
Hjalmar Rosengren's user avatar
3 votes
0 answers
115 views

Reference for the Netto's theorem on the permutation groups which was mentioned in the paper of Frobenius

I'm trying to read 'Uber die Charaktere der mehrfach transitiven Gruppen' written by Frobenius. There he mentioned some theorems of Netto. I'm depending on the Google translator. and the translation ...
gualterio's user avatar
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1 vote
0 answers
213 views

Is there any research on the action of a subgroup on the whole finite group by conjugation?

I want to know whether there are any research on the orbits of the action of a subgroup by conjugation on the whole group, when the group is finite. (Especially whole symmetric group.) I'm especially ...
gualterio's user avatar
  • 1,013