Cohomology of uniformly powerful groups
Authors:
William Browder and Jonathan Pakianathan
Journal:
Trans. Amer. Math. Soc. 352 (2000), 26592688
MSC (1991):
Primary 20J06, 17B50; Secondary 17B56
Published electronically:
July 20, 1999
MathSciNet review:
1661313
Fulltext PDF Free Access
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Abstract: In this paper we will study the cohomology of a family of groups associated to Lie algebras. More precisely, we study a category of groups which will be equivalent to the category of bracket algebras (Lie algebras minus the Jacobi identity). We then show that for a group in this category, its cohomology is that of an elementary abelian group if and only if it is associated to a Lie algebra. We then proceed to study the exponent of in the case that is associated to a Lie algebra . To do this, we use the Bockstein spectral sequence and derive a formula that gives in terms of the Lie algebra cohomologies of . We then expand some of these results to a wider category of groups. In particular, we calculate the cohomology of the groups which are defined to be the kernel of the mod reduction
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 T. Weigel, Pcentral groups and Poincar duality, Trans. Amer. Math. Soc., to appear. CMP 98:12
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 T. Weigel, Exp and log functors for the categories of powerful pcentral groups and Lie algebras, Habilitationsschrift, Freiburg, 1994.
 [W4]
 T. Weigel, A note on the AdoIwasawa theorem, in preparation.
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Additional Information
William Browder
Affiliation:
Department of Mathematics, Princeton University, Princeton, New Jersey 085440001
Jonathan Pakianathan
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, Wisconsin 53706
DOI:
http://dx.doi.org/10.1090/S0002994799024708
PII:
S 00029947(99)024708
Received by editor(s):
January 16, 1998
Published electronically:
July 20, 1999
Article copyright:
© Copyright 2000
American Mathematical Society
