132 research outputs found
Splittings of generalized Baumslag-Solitar groups
We study the structure of generalized Baumslag-Solitar groups from the point
of view of their (usually non-unique) splittings as fundamental groups of
graphs of infinite cyclic groups. We find and characterize certain
decompositions of smallest complexity (`fully reduced' decompositions) and give
a simplified proof of the existence of deformations. We also prove a finiteness
theorem and solve the isomorphism problem for generalized Baumslag-Solitar
groups with no non-trivial integral moduli.Comment: 20 pages; hyperlinked latex. Version 2: minor change
Discriminating Groups
A group G is termed discriminating if every group separated by G is discriminated by G. In this paper we answer several questions concerning discrimination which arose from [2]. We prove that a finitely generated equationally Noetherian group G is discriminating if and only if the quasivariety generated by G is the minimal universal class containing G. Among other results, we show that the non-abelian free nilpotent groups are non-discriminating. Finally we list some open problems concerning discriminating groups
Applications of p-deficiency and p-largeness
We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of
p-largeness to show that a group having a finite presentation with p-deficiency
greater than 1 is large, which implies that Schlage-Puchta's infinite finitely
generated p-groups are not finitely presented. We also show that for all primes
p at least 7, any group having a presentation of p-deficiency greater than 1 is
Golod-Shafarevich, and has a finite index subgroup which is Golod-Shafarevich
for the remaining primes. We also generalise a result of Grigorchuk on Coxeter
groups to odd primes.Comment: 23 page
Compact -deformation and spectral triples
We construct discrete versions of -Minkowski space related to a
certain compactness of the time coordinate. We show that these models fit into
the framework of noncommutative geometry in the sense of spectral triples. The
dynamical system of the underlying discrete groups (which include some
Baumslag--Solitar groups) is heavily used in order to construct \emph{finitely
summable} spectral triples. This allows to bypass an obstruction to
finite-summability appearing when using the common regular representation. The
dimension of these spectral triples is unrelated to the number of coordinates
defining the -deformed Minkowski spaces.Comment: 30 page
Schreier rewriting beyond the classical setting
Using actions of free monoids and free associative algebras, we establish
some Schreier-type formulas involving the ranks of actions and the ranks of
subactions in free actions or Grassmann-type relations for the ranks of
intersections of subactions of free actions. The coset action of the free group
is used to establish the generalization of the Schreier formula to the case of
subgroups of infinite index. We also study and apply large modules over free
associative algebras in the spirit of the paper Olshanskii, A. Yu.; Osin, D.V.,
Large groups and their periodic quotients, Proc. Amer. Math. Soc., 136 (2008),
753 - 759.Comment: 17 page
Folic Acid Supplementation and Spontaneous Preterm Birth: Adding Grist to the Mill?
Nicholas Fisk and colleagues discuss a new study reporting that additional voluntary folic acid supplementation was associated with a major reduction in very preterm births
Traditional use of the Andean flicker (Colaptes rupicola) as a galactagogue in the Peruvian Andes
This paper explores the use of the dried meat and feathers of the Andean Flicker (Colaptes rupicola) to increase the milk supply of nursing women and domestic animals in the Andes. The treatment is of preColumbian origin, but continues to be used in some areas, including the village in the southern Peruvian highlands where I do ethnographic research. I explore the factors giving rise to and sustaining the practice, relate it to other galactagogues used in the Andes and to the use of birds in ethnomedical and ethnoveterinary treatments in general, and situate it within the general tendency in the Andes and elsewhere to replicate human relations in the treatment of valuable livestock. The bird's use as a galactagogue appears to be motivated by both metaphorical associations and its perceived efficacy, and conceptually blends human and animal healthcare domains
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