By C. Allday, V. Puppe (auth.), Stefan Jackowski, Krzysztof Pawałowski (eds.)
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Additional resources for Transformation Groups Poznań 1985: Proceedings of a Symposium held in Poznań, July 5–9, 1985
Is that the c a t e g o r y which arise as h o m o l o g y of the c a t e g o r y worthwhile of integral (cohomology) (modular) as the c o m p l e x i t y some steps and (Sec. our feeof is an important its a l g e b r a i c The p r o j e c t i v i t y criterions side, representations of G - s p a c e s of all r e p r e s e n t a t i o n s , in its own right. well criterion study (Thm. 1) 3) and their c o n s e q u e n c e s as are in this direction. In c o m p a r i n g Question On the a l g e b r a i c 3.
M for some , and t ~ 0 Let us refer to this c o n s t r u c t i o n as "an ~ - c o m p o s i t e extension". 5 Corollary. Suppose that i , and suppose X Hi(X;k) = 0 for all s u f f i c i e n t l y large has a h o m o t o p y G - a c t i o n ~ : G ~ E(X) . Then (X,~) is e q u i v a l e n t to a topological G - a c t i o n only if some m - c o m p o s i t e extension L by a mod of the k G - m o d u l e s k Moore G-space. Hi(X;k) (as given by ~ ) is r e a l i z a b l e m While this c o r o l l a r y seems to be a formal c o n s e q u e n c e of definitions, it does lead to the following t h e o r e m which will be p r o v e d in section 5.
And ring and G RG 6 Sylow(G) Sylow(G) P be the group algebra over logical p r o p e r t i e s of RG-modules, standing of p r o j e c t i v e modules. (I) Rim : A X G - m o d u l e (21 C h o u i n a r d projective  Let R be a R . In studying the cohomo- it is n e c e s s a r y to have a good under- The f o l l o w i n g two theorems have played important roles in the " l o c a l - t o - g l o b a l " ~Gp-projective for a l l denotes the set of S y l o w sub- denotes a p - S y l o w subgroup.