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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Cohomological dimension of a group with respect to finite modules

Author: Juan José Martínez
Journal: Trans. Amer. Math. Soc. 226 (1977), 191-201
MSC: Primary 20J05
MathSciNet review: 0437654
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Abstract: The purpose of this paper is to compare the cohomological dimension of a group, relative to finite modules, with the cohomological dimension, in the usual sense, of its profinite completion. The basic tool used to perform this comparison is certain stable cohomology of the group. The reason is that there exists a spectral sequence which relates the continuous cohomology of the profinite completion, with coefficients in this stable cohomology, to the ordinary cohomology of the group. Moreover, the direct method of connecting the cohomology of the group with the profinite cohomology of its completion arises from the edge effects on the base of this spectral sequence.

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Keywords: Profinite completion of a group, stable cohomology of a group, spectral sequence, cohomological dimension of a group, stable dimension of a group, cohomological dimension of a profinite group
Article copyright: © Copyright 1977 American Mathematical Society

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