The indecomposability of a certain bimodule given by the Brauer construction

Broué’s abelian defect conjecture [3, 6.2] predicts for a p-block of a finite group G with an abelian defect group P a derived equivalence between the block algebra and its Brauer correspondent. By a result of Rickard [11], such a derived equivalence would in particular imply a stable equivalence induced by tensoring with a suitable bimodule - and it appears that these stable equivalences in turn tend to be obtained by “gluing” together Morita equivalences at the local levels of the considered blocks; see e.g. [4, 6.3], [8, 3.1], [12, 4.1], and [13, 5.6, A.4.1]. This note provides a technical indecomposability result which is intended to verify in suitable circumstances the hypotheses that are necessary to apply gluing results as mentioned above. This is used in [7] to show that Broué’s abelian defect group conjecture holds for nonprincipal blocks of the simple Held group and the sporadic Suzuki group

Considerations of some critical ejector problems

Some aspects of ejector design and application, including, three dimensional effects and cross flow effects are presented