. A uniform and constructive approach for the computation of resolutions and for (co)homology computations for any nite p-group is detailed. The resolutions we construct ([32]) are, as vector spaces, as small as the minimal resolution of IFp over the elementary abelian p-group of the same order as the group under study. Our implementations are based on the development of sophisticated algebraic data structures. Applications to calculating functional cocycles are given and the possibility of constructing interesting codes using such methods is presented. 1 Introduction In this paper, we present a uniform constructive approach to calculating relatively small resolutions over nite p-groups. The algorithm we use comes from [32, 8.1.8 and the penultimate paragraph of 9.4]. There has been a massive amount of work done on the structure of p-groups since the beginning of group theory. A good introduction is [22]. We combine mathematical and computer methods to construct the uniform resolut...

A uniform and constructive approach for the computation of resolutions and for (co)homology computations for any nite p-group is detailed. The resolutions we construct ([29]) are, as vector spaces, as small as the minimal resolution of IFp over the elementary abelian p-group of the same order as the group under study. Our implementations are based on the development of sophisticated algebraic data structures. Applications to calculating functional cocycles are given and the possibility of constructing interesting codes using such methods is presented. 1

In [3] "mall" 1-homological model H of a commutative differential graded algebra is described. Homological Perturbation Theory (HPT) [7-9] provides an explicit description of an A1-coalgebra structure ( 1 ; 2 ; 3 ; : : :) of H. In this paper, we are mainly interested in the determination of the map 2 : H ! H H as a first step in the study of this structure. Developing the techniques given in [20] (inversion theory), we get an important improvement in the computation of 2 with regard to the first formula given by HPT. In the case of purely quadratic algebras, we sketch a procedure for giving the complete Hopf algebra structure of its 1-homology.