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On extended block induction and Brauer’s third main theorem. (English) Zbl 0907.20019
Solomon, Ronald (ed.), Representation theory of finite groups. Proceedings of a special research quarter, Columbus, OH, USA, Spring 1995. Dedicated to Walter Feit on the occasion of his sixty-fifth birthday. Berlin: de Gruyter. Ohio State Univ. Math. Res. Inst. Publ. 6, 85-91 (1997).
This paper considers four different definitions (Definition (1)) of block induction which have been proposed and used in studying modular representation theory of finite groups; namely: Brauer induction, $$p$$-regular induction, extended induction and Alperin-Burry induction. Among those definitions, extended block induction is the weakest. This paper examines whether properties of other types of induction also hold for extended induction. For example, it is shown (§4) that the transitivity which holds along blocks under Brauer induction and $$p$$-regular induction does not hold under extended induction.
For the entire collection see [Zbl 0883.00016].
##### MSC:
 20C20 Modular representations and characters