The extension of the first main theorem for \(\pi\)-blocks.
Let \(\pi\) be a set of primes, and let \(D\) be a normal \(\pi\)-subgroup of a finite \(\pi\)-separable group \(G\). The author shows that the \(\pi\)-blocks of \(G\) with defect group \(D\) are in bijection with the \(G\)-orbits of \(\pi\)-blocks \(b\) of \(H=DC_G(D)\) with defect group \(D\) such that \(|I_G(b):H|_\pi=1\); here \(I_G(b)\) denotes the stabilizer of \(b\) in \(G\).
scientific article; zbMATH DE number 5118295