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.
Lecture Notes in Mathematics Editors: J.--M. Morel, Cachan F. Takens, Groningen B. Teissier, Paris
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3 Berlin Heidelberg New York Hong Kong London Milan Paris Tokyo
David J. Green
Gr¨obner Bases and the Computation of Group Cohomology
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Author David J. Green FB C - Mathematik und Naturwissenschaften Bergische Universit¨at Wuppertal Gaussstr. 20 42097 Wuppertal Germany e-mail:
[email protected]
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Mathematics Subject Classification (2000): 20J06, 16S15, 16E05, 16Z05, 20C05, 20D15 ISSN 0075-8434 ISBN 3-540-20339-7 Springer-Verlag Berlin Heidelberg New York This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specif ically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microf ilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use mu