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More about the (co)homology of groups and associative algebras
#
More about the (co)homology of groups and associative algebras

##
Hvedri Inassaridze

It is proved that the homology and cohomology theories of groups
and associative algebras are non-abelian derived functors of the
cokernel and kernel groups of higher dimensions of their defining
standard chain and cochain complexes respectively. The same
results are also obtained for the relative (co)homology of groups,
the mod q cohomology of groups and the cohomology of groups with
operators. This allowed us to give an alternative approach to
higher Hopf formulas for integral homology of groups. An axiomatic
characterization of the relative cohomology of groups is given and
higher relative $(n+1)$-th cohomology of groups is described in
terms of n-fold extensions.

Homology, Homotopy and Applications, Vol. 7(2005), No. 1, pp. 87-108
http://www.rmi.acnet.ge/hha/volumes/2005/n1a6/v7n1a6.dvi (ps, dvi.gz, ps.gz, pdf)
ftp://ftp.rmi.acnet.ge/pub/hha/volumes/2005/n1a6/v7n1a6.dvi (ps, dvi.gz, ps.gz, pdf)