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Relative Projectivity of Modules and Cohomology Theory of Finite Groups

Research paper by Tetsuro Okuyama, Hiroki Sasaki

Indexed on: 01 Dec '01Published on: 01 Dec '01Published in: Algebras and Representation Theory



Abstract

In the modular representation theory of finite groups the theory of projectivity relative to subgroups is of fundamental importance. To generalize this notion the theory of projectivity relative to “modules” was introduced by the first author. Our aim is to show some aspects of cohomology theory of finite groups concerning projectivity of modules relative to both subgroups and modules. We shall give some applications to the cohomology theory; especially we shall calculate the mod 2 cohomology algebras of finite groups with wreathed Sylow 2-subgroups.