Abstract
Abstract In the modular representation theory of finite groups, we show that the standard derivation of the Green correspondence lifts to a derivation of a Green correspondence for twisted group algebras (Theorem 1.3). Then, from these results we derive a lift of the Puig correspondences for twisted group algebras (Theorem 1.6). Clearly twisted group algebras arise naturally in finite group modular representation theory. We conclude with some suggestions for applications in this mathematical area.
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