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8 votes
0 answers
190 views

Groups having exactly two non real-valued irreducible characters

This is an enlarged version of my question on MSE. It was suggested I ask here instead. Suppose the finite group $G$ has exactly two conjugacy classes that are not self-inverse (a conjugacy class is ...
3 votes
1 answer
1k views

Conditions for a solvable group to have a non-trivial center

I am working on a problem in character theory where I try to bound the derived length of a solvable group using information about its characters. In my specific case, it will be extremely helpful for ...