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.
Gröbner Bases and the Computation of Group Cohomology
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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.
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Inside This Book
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First Sentence:
Let G be a p-group and k a field of characteristic p. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
inclusion ambiguity, resolvable relative, inclusion ambiguities, elementary abelian subgroup, diamond lemma, regular generators, cohornology ring, graded commutative algebras, cohomology ring, minimal generators, minimal resolution, minimal generating set, nilpotent element, small group number, monomial ideal, criterion detects, completeness criterion, essential ideal, essential classes, minimal relations, free generators, generator degrees, group cohomology, maximal subgroups, projective resolution Key Phrases - Capitalized Phrases (CAPs): (learn more)
Buchberger Algorithm, Diamond Lemma, Assume Hypothesis, Nilradical There, Bucliberger Algorithm, Carlson's Koszul, Hall Senior, Perform Expand, Suppose Hypothesis New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Let G be a p-group and k a field of characteristic p. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
inclusion ambiguity, resolvable relative, inclusion ambiguities, elementary abelian subgroup, diamond lemma, regular generators, cohornology ring, graded commutative algebras, cohomology ring, minimal generators, minimal resolution, minimal generating set, nilpotent element, small group number, monomial ideal, criterion detects, completeness criterion, essential ideal, essential classes, minimal relations, free generators, generator degrees, group cohomology, maximal subgroups, projective resolution Key Phrases - Capitalized Phrases (CAPs): (learn more)
Buchberger Algorithm, Diamond Lemma, Assume Hypothesis, Nilradical There, Bucliberger Algorithm, Carlson's Koszul, Hall Senior, Perform Expand, Suppose Hypothesis New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 36
books:
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- Geometric Curve Evolution and Image Processing (Lecture Notes in Mathematics) by Frédéric Cao in Back Matter
- The Decomposition of Primes in Torsion Point Fields (Lecture Notes in Mathematics) by Clemens Adelmann in Back Matter
- Continuous Bounded Cohomology of Locally Compact Groups (Lecture Notes in Mathematics) by Nicolas Monod in Back Matter
- Moment Theory and Some Inverse Problems in Potential Theory and Heat Conduction (Lecture Notes in Mathematics) by Dang D. Ang in Back Matter
- Grothendieck Duality and Base Change (Lecture Notes in Mathematics) by Brian Conrad in Back Matter
See all 36 books this book cites
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