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In an earlier paper (Turull, 2012 [12]) the author introduced the concept of endoisomorphisms and showed its natural connection with Clifford theory of finite groups. Associated with Clifford theory are module and character correspondences. In the present paper the author shows that each endoisomorphism produces a unique module and character correspondence with excellent compatibility results.
The Alperin–McKay conjecture is a well-known conjecture. It is known to be true for p-solvable groups by work of Dade and Okuyama–Wajima. Recently, this conjecture has been strengthened by work of Isaacs–Navarro, Navarro and Turull. This refinement involves the degrees modulo p of the characters involved, the field of values over the p-adic numbers of the relevant characters, and their p-local Schur...
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