Titlebook: Syzygies and Homotopy Theory; F.E.A. Johnson Book 2012 Springer-Verlag London Limited 2012 D(2) problem.Milnor squares.R(2) problem.genera

只看該作者 · 發(fā)表于 2025-3-26 03:35:08

Group Rings of Dihedral Groupsrder 2. defined by the presentation . Our main result, first proved in Johnson (Q. J. Math., ., doi:.), is that .[..×..] has SFC when . is an odd prime. This breaks down for .=2. Although .[..×..] still has SFC (the case .=1) when .≥2 a result of O’Shea shows that .[..×..] has infinitely many isomorphically distinct stably free modules of rank 1.

只看該作者 · 發(fā)表于 2025-3-26 05:14:39

Parametrizing ,,(,): Singular Casehat .. Then . is necessarily infinite. We investigate minimality of . in ..(.) and first establish: . This second criterion also applies to many cases where . although we do not need to use it there. We employ it in Sect.?. to give examples of groups . with infinite splitting in ..(.).

只看該作者 · 發(fā)表于 2025-3-26 12:06:07

Conclusionis (Edwards in Ph.D. Thesis, University College London, .; in Algebr. Geom. Topol. 6:71–89, .). The account given here simplifies Edwards’ argument at a number of points. We then present some duality results for higher syzygies. We conclude by giving a survey of the current status of the .–. problem.

只看該作者 · 發(fā)表于 2025-3-26 13:49:40

只看該作者 · 發(fā)表于 2025-3-26 19:22:57

https://doi.org/10.1007/978-1-4471-2294-4D(2) problem; Milnor squares; R(2) problem; generalized Swan module; stable module; syzygy

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