On stable equivalences of Morita type and nilpotent blocks (Q6667408)

Nilpotent blocks were introduced by \textit{M. Broué} and \textit{L. Puig} in [Invent. Math. 56, 117--128 (1980; Zbl 0425.20008)] to give a representation-theoretic analogue of Frobenius' result on \(p\)-nilpotent groups. Stable equivalences of Morita type was introduced by \textit{M. Broué} (in [NATO ASI Ser., Ser. C, Math. Phys. Sci. 424, 1--26 (1994; Zbl 0827.20007)]) after the similar results for derived equivalences by \textit {J. Rickard} [J. Lond. Math. Soc., II. Ser. 39, No. 3, 436--456 (1989; Zbl 0642.16034)]. \textit{L. Puig}, in [On the local structure of Morita and Rickard equivalences between Brauer blocks. Basel: Birkhäuser (1999; Zbl 0929.20012)], proved that blocks which are stable equivalent of Morita type to nilpotent blocks are also nilpotent by showing that such stable equivalences are induced by bimodules with endopermutation sources.\N\NIn the paper under review the author provides a new proof for Puig's theorem using module-theoretic methods.