The lower central and derived series of the braid groups of the projective plane

In this paper, we determine the lower central and derived series for the braid groups of the projective plane. We are motivated in part by the study of Fadell-Neuwirth short exact sequences, but the problem is interesting in its own right. The n-string braid groups B(n)(RP(2)) of the projective plane RP(2) were originally studied by Van Buskirk during the 1960s. and are of particular interest due to the fact that they have torsion. The group B(1)(RP(2)) (resp. B(2)(RP(2))) is isomorphic to the cyclic group Z(2) of order 2 (resp. the generalised quaternion group of order 16) and hence their lower central and derived series are known. If n > 2, we first prove that the lower central series of B(n)(RP(2)) is constant from the commutator subgroup onwards. We observe that Gamma(2)(B(3)(RP(2))) is isomorphic to (F(3) X Q(8)) X Z(3), where F(k) denotes the free group of rank k, and Q(8) denotes the quaternion group of order 8, and that Gamma(2)(B(4)(RP(2))) is an extension of an index 2 subgroup K of P(4)(RP(2)) by Z(2) circle plus Z(2). As for the derived series of B(n)(RP(2)), we show that for all n >= 5, it is constant from the derived subgroup onwards. The group B(n)(RP(2)) being finite and soluble for n <= 2, the critical cases are n = 3, 4. We are able to determine completely the derived series of B(3)(RP(2)). The subgroups (B(3)(RP(2)))((1)), (B(3)(RP(2)))((2)) and (B(3)(RP(2)))((3)) are isomorphic respectively to (F(3) x Q(8)) x Z(3), F(3) X Q(8) and F(9) X Z(2), and we compute the derived series quotients of these groups. From (B(3)(RP(2)))((4)) onwards, the derived series of B(3)(RP(2)), as well as its successive derived series quotients, coincide with those of F(9). We analyse the derived series of B(4)(RP(2)) and its quotients up to (B(4)(RP(2)))((4)), and we show that (B(4)(RP(2)))((4)) is a semi-direct product of F(129) by F(17). Finally, we give a presentation of Gamma(2)(B(n)(RP(2))). (C) 2011 Elsevier Inc. All rights reserved.

Star-group identities and groups of units

Analogous to *-identities in rings with involution we define *-identities in groups. Suppose that G is a torsion group with involution * and that F is an infinite field with char F not equal 2. Extend * linearly to FG. We prove that the unit group U of FG satisfies a *-identity if and only if the symmetric elements U(+) satisfy a group identity.

Locally nilpotent groups of units in tiled rings

We consider locally nilpotent subgroups of units in basic tiled rings A, over local rings O which satisfy a weak commutativity condition. Tiled rings are generalizations of both tiled orders and incidence rings. If, in addition, O is Artinian then we give a complete description of the maximal locally nilpotent subgroups of the unit group of A up to conjugacy. All of them are both nilpotent and maximal Engel. This generalizes our description of such subgroups of upper-triangular matrices over O given in M. Dokuchaev, V. Kirichenko, and C. Polcino Milies (2005) [3]. (C) 2010 Elsevier Inc. All rights reserved.

Braid groups of non-orientable surfaces and the Fadell-Neuwirth short exact sequence

Let M be a compact, connected non-orientable surface without boundary and of genus g >= 3. We investigate the pure braid groups P,(M) of M, and in particular the possible splitting of the Fadell-Neuwirth short exact sequence 1 -> P(m)(M \ {x(1), ..., x(n)}) hooked right arrow P(n+m)(M) (P*) under right arrow P(n)(M) -> 1, where m, n >= 1, and p* is the homomorphism which corresponds geometrically to forgetting the last m strings. This problem is equivalent to that of the existence of a section for the associated fibration p: F(n+m)(M) -> F(n)(M) of configuration spaces, defined by p((x(1), ..., x(n), x(n+1), ..., x(n+m))) = (x(1), ..., x(n)). We show that p and p* admit a section if and only if n = 1. Together with previous results, this completes the resolution of the splitting problem for surface pure braid groups. (C) 2009 Elsevier B.V. All rights reserved.

Classification of the virtually cyclic subgroups of the pure braid groups of the projective plane

We classify the ( finite and infinite) virtually cyclic subgroups of the pure braid groups P(n)(RP(2)) of the projective plane. The maximal finite subgroups of P(n)(RP(2)) are isomorphic to the quaternion group of order 8 if n = 3, and to Z(4) if n >= 4. Further, for all n >= 3, the following groups are, up to isomorphism, the infinite virtually cyclic subgroups of P(n)(RP(2)): Z, Z(2) x Z and the amalgamated product Z(4)*(Z2)Z(4).

What is important for you? A qualitative interview study of living with diabetes and experiences of diabetes care to establish a basis for a tailored Patient-Reported Outcome Measure for the Swedish National Diabetes Register

OBJECTIVES: There is a growing emphasis on the perspective of individuals living with diabetes and the need for a more person-centred diabetes care. At present, the Swedish National Diabetes Register (NDR) lacks patient-reported outcome measures (PROMs) based on the perspective of the patient. As a basis for a new PROM, the aim of this study was to describe important aspects in life for adult individuals with diabetes. DESIGN: Semistructured qualitative interviews analysed using content analysis. SETTING: Hospital-based outpatient clinics and primary healthcare clinics in Sweden. PARTICIPANTS: 29 adults with type 1 diabetes mellitus (DM) (n=15) and type 2 DM (n=14). INCLUSION CRITERIA: Swedish adults (≥18 years) living with type 1 DM or type 2 DM (duration ≥5 years) able to describe their situation in Swedish. Purposive sampling generated heterogeneous characteristics. RESULTS: To live a good life with diabetes is demanding for the individual, but experienced barriers can be eased by support from others in the personal sphere, and by professional support from diabetes care. Diabetes care was a crucial resource to nurture the individual's ability and knowledge to manage diabetes, and to facilitate life with diabetes by supplying support, guidance, medical treatment and technical devices tailored to individual needs. The analysis resulted in the overarching theme 'To live a good life with diabetes' constituting the two main categories 'How I feel and how things are going with my diabetes' and 'Support from diabetes care in managing diabetes' including five different categories. CONCLUSIONS: Common aspects were identified including the experience of living with diabetes and support from diabetes care. These will be used to establish a basis for a tailored PROM for the NDR.

Cortical diversity in three species groups of Parmotrema sensu lato (Parmeliaceae, lichenized Ascomycota)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Diet and trophic groups of an aquatic insect community in a tropical stream

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Conserved Karyotypes in Cophomantini: Cytogenetic Analysis of 12 Species from 3 Species Groups of Bokermannohyla (Amphibia: Anura: Hylidae)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Is the evolutionary history of the O-type P element in the saltans and willistoni groups of Drosophila similar to that of the canonical P element?

We studied the occurrence of O-type P elements in at least one species of each subgroup of the saltans group, in order to better understand the phylogenetic relationships among the elements within the saltans group and with those of species belonging to the willistoni group. We found that the O-type subfamily has a patchy distribution within the saltans group (it does not occur in D. neocordata and D. emarginata), low sequence divergence among species of the saltans group as well as in relation to species of the willistoni group, a lower rate of synonymous substitution for coding sequences compared to Adh, and phylogenetic incongruities. These findings suggest that the evolutionary history of the O-type subfamily within the saltans and willistoni groups follows the same model proposed for the canonical subfamily of P elements, i.e., events of horizontal transfer between species of the saltans and willistoni groups.

Simultaneous Determination of Two Groups of Elements in Milk by Electrothermal Atomic Absorption Spectrometry: Evaluation of Ruthenium Modifiers

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Morphological variation in two genetically distinct groups of the golden-striped salamander, Chioglossa lusitanica (Amphibia : Urodela)

Morphometric and colour pattern variation in the endemic Iberian salamander Chioglosso lusitanica is concordant with the genetic differentiation of two groups of populations separated by the Mondego river ill Portugal. Salamanders from the south have shorter digits than those from the north. Clinal variation with a south to north increase in limb. toe and finger length was found superiniposed on this dichotomy resulting in stepped clines for characters describing appendage size. Genetic variability was paralleled by colour pattern variability in the contact zone and in northern populations. To explain the observed parallels we invoke the neutral processes of vicariant isolation. admixture in a secondary contact zone, genetic drift in addition to selection acting along all environmental gradient. Morphological constraints imposed by a highly specialized ecological niche may explain why the genetic subdivision of C. lusitanica since the early, Pleistocene has remained fairly cryptic.

Isotopic characterization of the metabasites and amphibolites of the Acungui and Setuva Groups of the Ribeira Belt

Pb, Rb, Sr, Sm and Nd isotope analyses were carried out on amphibolitic rocks from Campo Largo (PR), Rio Branco do Sul (PR) and Adrianópolis (PR) and for the metabasite from Adrianópolis and Apiai (SP), all belonging to the Açungui and Setuva Groups, southern portion of the Ribeira Belt. These occurrences were chosen because each exhibits geochemical data indicative of a mantle source, having different signatures. Geochronologic determinations are available only for the Apiai metagabbro with Neoproterozoic ages of 617 ± 4 Ma (U/Pb in zircon) and 839 ± 85 Ma (Rb/Sr, whole rock). Age determinations by Sm/Nd mineral isochron using whole rock, plagioclase and pyroxene yield values of 885 ± 53 Ma for the Apiai metagabbro and 820 ± 84 Ma for the Adrianópolis metabasite. These results agree within error with the Rb/Sr isochron of 839 ± 85 Ma may possibly be interpreted as the time of extraction of the magma from the mantle, as suggested by positive εNd(850) values (+2,76) from an Adrianópolis sample. An εNd values versus 87Sr/86Sr diagram shows that each studied occurrence plots in a different position, following approximately the mantle array trend, the most primitive being the metabasite of Adrian-acopolis, near the MORB field, and the most enriched being the amphibolite from the same region, near the enriched mantle and or crustal contamination field. The distinct difference in isotopic signatures between the amphibolite and metabasite suggests derivation from different mantle sources, as supported by available geochemical data. Nevertheless, some of the samples show isotopic evidence of the action of metamorphism, crustal contamination and weathering.

2010-2011 programme of work of the working groups of the Statistical Conference of the Americas of ECLAC

Includes bibliography