On generalizations of the McKay Conjecture

McKay Conjecture asserts the existence of a one-to-one correspondence between sets of certain irreducible characters of any group and that of its local subgroups. In this thesis, we mainly study two generalizations of this conjecture, known as Isaacs-Navarro and Galois-McKay conjectures, along with their reductions to finite simple groups. The former considers the original conjecture via considering equivalence classes in mod p whereas the other takes into account a particular action of a Galois group. Also, we construct some new H-triples following [1].