Gröbner Bases and the Computation of Group Cohomology

David J. Green (auth.)3540203397, 9783540203391

This monograph develops the Gröbner basis methods needed to perform efficient state of the art calculations in the cohomology of finite groups. Results obtained include the first counterexample to the conjecture that the ideal of essential classes squares to zero. The context is J. F. Carlson’s minimal resolutions approach to cohomology computations.

Table of contents :
Introduction….Pages 1-9
Part I: 1 Bases for finite-dimensional algebras and modules….Pages 13-20
Part I: 2 The Buchberger Algorithm for modules….Pages 21-32
Part I: 3 Constructing minimal resolutions….Pages 33-46
Part II: 4 Gröbner bases for graded commutative algebras….Pages 49-65
Part II: 5 The visible ring structure….Pages 67-80
Part II: 6 The completeness of the presentation….Pages 81-90
Part III: 7 Experimental results….Pages 93-100
A Sample cohomology calculations….Pages 101-130
Epilogue and References….Pages 131-135