Ordinary induction from a subgroup and finite group block theory

Abstract

The first step in the fundamental Clifford Theoretic Approach to General Block Theory of Finite Groups reduces to: $H$ is a subgroup of the finite group $G$ and $b$ is a block of $H$ such that $b({}^{g} b)=0$ for all $g\in G-H$. We extend basic results of several authors in this situation and place these results into current categorical and character theoretic equivalences frameworks.