Glasgow Mathematical Journal



Higher non-abelian cohomology of groups


Hvedri Inassaridze a1
a1 A. Razmadze Matematical Institute, Georgian Academy of Sciences, Georgia e-mail: hvedri@rmi.acnet.ge URL: http://www.rmi.acnet.ge/~hvedri/

The first non-abelian cohomology of groups introduced by Guin is extended to any dimensions and for a substantially wider class of coefficients called G-partially crossed P-modules. The first and the second non-abelian cohomologies of groups are described in terms of torsors and extensions of groups respectively. Higher non-abelian cohomology pointed sets are described in terms of cotriple right derived functors of the group of derivations with respect to the first contravariant variable. For any short exact coefficient sequence a long exact cohomology sequence is obtained extending the well-known exact cohomology sequences and higher cohomology of groups with coefficients in any G-group is introduced.

(Received February 21 2001)
(Accepted July 17 2001)