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We study groups whose cohomology functors commute with filtered colimits in high dimensions. We relate this condition to the existence of projective resolutions which exhibit some finiteness properties in high dimensions, and to the existence of Eilenberg–Mac Lane spaces with finitely many n-cells for all sufficiently large n. To that end, we determine the structure of completely finitary Gorenstein projective modules over group rings. The methods are inspired by representation theory and make use of the stable module category, in which morphisms are defined through complete cohomology. In order to carry out these methods, we need to restrict ourselves to certain classes of hierarchically decomposable groups. 相似文献
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P. H. Kropholler S. J. Pride W. A. M. Othman K. B. Wong P. C. Wong 《Semigroup Forum》2010,81(1):172-186
In this paper, we study some properties of semigroups with presentation 〈a,b ; a
p
=b
r
,a
q
=b
s
〉. We will also study their potential as platforms for the Diffie-Hellman key exchange protocol. 相似文献
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Geometriae Dedicata - We build on the constructions in Brady (J Lond Math Soc 60(2):461–480, 1999) and Lodha (A hyperbolic group with a finitely presented subgroup that is not of type FP3,... 相似文献
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E. Hrushovski P. H. Kropholler A. Lubotzky A. Shalev 《Transactions of the American Mathematical Society》1996,348(1):291-304
In this paper we study the set of -powers in certain finitely generated groups . We show that, if is soluble or linear, and contains a finite index subgroup, then is nilpotent-by-finite. We also show that, if is linear and has finite index (i.e. may be covered by finitely many translations of ), then is soluble-by-finite. The proof applies invariant measures on amenable groups, number-theoretic results concerning the -unit equation, the theory of algebraic groups and strong approximation results for linear groups in arbitrary characteristic.
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Let G be a locally finite group of cardinality n where n isa natural number. Let (G) be the set of primes p for which Ghas an element of order p. In [5], Holt conjectures that ifk is a finite field with char k (G) then (1) G has cohomological dimension n+1 over k; (2) Hn+1(G, kG) has cardinality 2n; (3) Hi(G, kG) = 0 for 0 i n. 相似文献
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It is shown that every H
-group G of type admits a finite dimensional G-CW-complex X with finite stabilizers and with the additional property that for each finite subgroup H, the fixed point subspace X
H
is contractible. This establishes conjecture (5.1.2) of [9]. The construction of X involves joining a family of spaces parametrized by the poset of non-trivial finite subgroups of G and ultimately relies on the theorem of Cornick and Kropholler that if M is a -module which is projective as a -module for all finite then M has finite projective dimension.
Received: April 30, 1997 相似文献
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