617 research outputs found
Cohomological finiteness conditions for a class of metabelian groups
We consider a class of metabelian groups first studied by Baumslag and
Stammbach and we show that these groups are consistent with the Bieri-Groves
conjecture which relates cohomological finiteness conditions to the
Bieri-Neumann-Strebel sigma invariant.Comment: 10 pages Accepted for publication in the Bulletin of the London
Mathematical Societ
A Sufficient Condition for Nilpotency in a Finite Group
It is shown that finite groups in which the order of the product of every
pair of elements of co-prime order is the product of the orders, is nilpotent
The acyclic group dichotomy
Two extremal classes of acyclic groups are discussed. For an arbitrary group
G, there is always a homomorphism from an acyclic group of cohomological
dimension 2 onto the maximum perfect subgroup of G, and there is always an
embedding of G in a binate (hence acyclic) group. In the other direction, there
are no nontrivial homomorphisms from binate groups to groups of finite
cohomological dimension. Binate groups are shown to be of significance in
relation to a number of important K-theoretic isomorphism conjectures.Comment: To appea
Finitely presented subgroups of automatic groups and their isoperimetric functions
We describe a general technique for embedding certain amalgamated products
into direct products. This technique provides us with a way of constructing a
host of finitely presented subgroups of automatic groups which are not even
asynchronously automatic. We can also arrange that such subgroups satisfy, at
best, an exponential isoperimetric inequality.Comment: DVI and Post-Script files only. To appear in J. London Math. So
Counting homomorphisms onto finite solvable groups
We present a method for computing the number of epimorphisms from a
finitely-presented group G to a finite solvable group \Gamma, which generalizes
a formula of G\"aschutz. Key to this approach are the degree 1 and 2 cohomology
groups of G, with certain twisted coefficients. As an application, we count
low-index subgroups of G. We also investigate the finite solvable quotients of
the Baumslag-Solitar groups, the Baumslag parafree groups, and the Artin braid
groups.Comment: 30 pages; accepted for publication in the Journal of Algebr
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