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TitleGrรถbner Bases and the Computation of Group Cohomology [electronic resource]
ImprintBerlin, Heidelberg : Springer Berlin Heidelberg, 2003
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Descript XII, 144 p. online resource


This monograph develops the Grรถbner 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


Introduction -- Part I Constructing minimal resolutions: Bases for finite-dimensional algebras and modules; The Buchberger Algorithm for modules; Constructing minimal resolutions -- Part II Cohomology ring structure: Grรถbner bases for graded commutative algebras; The visible ring structure; The completeness of the presentation -- Part III Experimental results: Experimental results -- A. Sample cohomology calculations -- Epilogue -- References -- Index

Mathematics Associative rings Rings (Algebra) Group theory Mathematics Group Theory and Generalizations Associative Rings and Algebras


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