Relative cohomology of groups (original) (raw)

Lecture Notes in Mathematics, 1977

Abstract

I ° Introduction This talk is to present a few results on cohomology of groups arising from an investigation into the cohomological behaviour of inverse semigroups ([6], [7], [8]). In this context, relative cohomology in the sense of Auslander ([i]) is just a special case of a more general situation, and various long exact sequences, some of which are well-known ([9], [ii]) and have been established by various authors individually, can be obtained by one and the same method. The starting point for our consideration is the concept of a semilattice of groups, that is a functor S from a semilattice E regarded as a category to the category Gv of groups. Thus for e, f ( E , e ~_ f , there is exactly one group homomorphism ~e,f : S(e) ~ S(f) such that ~e,e is the identity on S(e) ,

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