Generalized soluble groups of finite co-central rank

Eine Gruppe G hat endlichen Prüferrang (bzw. Ko-zentralrang) kleiner gleich r, wenn für jede endlich erzeugte Gruppe H gilt: H (bzw. H modulo seinem Zentrum) ist r-erzeugbar. In der vorliegenden Arbeit werden, soweit möglich, die bekannten Sätze über Gruppen von endlichem Prüferrang (kurz X-Gruppen), auf die wesentlich größere Klasse der Gruppen mit endlichem Ko-zentralrang (kurz R-Gruppen) verallgemeinert.Für lokal nilpotente R-Gruppen, welche torsionsfrei oder p-Gruppen sind, wird gezeigt, dass die Zentrumsfaktorgruppe eine X-Gruppe sein muss. Es folgt, dass Hyperzentralität und lokale Nilpotenz für R-Gruppen identische Bediungungen sind. Analog hierzu sind R-Gruppen genau dann lokal auflösbar, wenn sie hyperabelsch sind. Zentral für die Strukturtheorie hyperabelscher R-Gruppen ist die Tatsache, dass solche Gruppen eine aufsteigende Normalreihe abelscher X-Gruppen besitzen. Es wird eine Sylowtheorie für periodische hyperabelsche R-Gruppen entwickelt. Für torsionsfreie hyperabelsche R-Gruppen wird deren Auflösbarkeit bewiesen. Des weiteren sind lokal endliche R-Gruppen fast hyperabelsch. Für R-Gruppen fallen sehr große Gruppenklassen mit den fast hyperabelschen Gruppen zusammen. Hierzu wird der Begriff der Sektionsüberdeckung eingeführt und gezeigt, dass R-Gruppen mit fast hyperabelscher Sektionsüberdeckung fast hyperabelsch sind.

Differenzierung von Reviergesängen und mitochondrialem Cytochrom-b in drei ausgewählten Singvogelgattungen (Aves, Passeriformes: Genus Regulus, Genus Seicercus und Parus major)

ZusammenfassungLautäußerungen von Singvögeln (Passeriformes) werden gemeinhin als Träger phylogenetischer Information betrachtet, obwohl direkte Nachweise in vergleichend bioakustischen Studien rar sind. Dieser Thematik widmet sich meine Dissertation am Beispiel dreier Singvogelgruppen: Goldhähnchen (Regulus), Goldbrillenlaubsänger (Seicercus) sowie verwandter Laubsänger (Phylloscopus) und Kohlmeisen (Parus major). Neben der Erhebung bioakustischer Daten wurde für jede Gruppe eine molekulare Phylogenie basierend auf Cytochrom-b-Sequenzen erstellt und für verschiedene akustische Merkmale Homoplasie-indizes berechnet (CI, RI und RC). Die phylogenetisch informativen Gesangsstrukturen innerhalb der Gattungen Regulus und Seicercus/ Phylloscopus sind sämtlich Syntaxmerkmale, zumeist der Gesamtstrophe, seltener von Strophenabschnitten. Bei den Goldhähnchen (Regulus) sind solche Syntaxmerkmale angeboren, Elementmerkmale hingegen sind erlernt und phylogenetisch nicht informativ. Die innerhalb der Kohlmeisen homogene Gesangssyntax ist erst auf höherer taxonomischer Ebene (Gattung Parus) ein informatives Merkmal. Der mittels einer Merkmalsmatrix berechnete akustische Divergenzindex zwischen Taxonpaaren steigt signifikant proportional zur genetischen Distanz. Damit ist erstmalig der Zusammenhang zwischen genetischer und akustischer Differenzierung quantifiziert. Die molekulare Phylogenie erhellt zudem bislang ungeklärte phylogenetische Beziehungen innerhalb aller drei Taxa. Diese werden im Hinblick auf das phylogenetische und das biologische Artkonzept diskutiert. Der Artstatus des Teneriffa-Goldhähnchens (Regulus teneriffae) sowie der bokharensis-Kohlmeisen ist fragwürdig aufgrund ihrer engen Verwandtschaft zu zu einzelnen Subspezies der Wintergoldhähnchen bzw. der Kohlmeisen.

Nearrings and a construction of triply factorized groups

In this thesis a connection between triply factorised groups and nearrings is investigated. A group G is called triply factorised by its subgroups A, B, and M, if G = AM = BM = AB, where M is normal in G and the intersection of A and B with M is trivial. There is a well-known connection between triply factorised groups and radical rings. If the adjoint group of a radical ring operates on its additive group, the semidirect product of those two groups is triply factorised. On the other hand, if G = AM = BM = AB is a triply factorised group with abelian subgroups A, B, and M, G can be constructed from a suitable radical ring, if the intersection of A and B is trivial. In these triply factorised groups the normal subgroup M is always abelian. In this thesis the construction of triply factorised groups is generalised using nearrings instead of radical rings. Nearrings are a generalisation of rings in the sense that their additive groups need not be abelian and only one distributive law holds. Furthermore, it is shown that every triply factorised group G = AM = BM = AB can be constructed from a nearring if A and B intersect trivially. Moreover, the structure of nearrings is investigated in detail. Especially local nearrings are investigated, since they are important for the construction of triply factorised groups. Given an arbitrary p-group N, a method to construct a local nearring is presented, such that the triply factorised group constructed from this nearring contains N as a subgroup of the normal subgroup M. Finally all local nearrings with dihedral groups of units are classified. It turns out that these nearrings are always finite and their order does not exceed 16.

Anatomy, phylogeny, and palaeoecology of the basal thalattosuchians (Mesoeucrocodylia) from the Liassic of Central Europe

In the marine Jurassic deposits of Europe, a group of marine crocodilians, the Thalattosuchia, belongs to the frequently found reptiles. Thalattosuchia are widely spread in Central Europe from the Jurassic to Lower Cretaceous, and some taxa are also distributed worldwide. The task of the work was to examine all taxa known from the Liassic of Europe. The most frequently known taxa Steneosaurus bollensis and Pelagosaurus typus are anatomically revised. New discoveries at the skull of Pelagosaurus typus e.g., the fact of a partly paired frontal are described by means of computed tomography investigations. In addition, juvenile specimens of this taxon are studied in detail for the first time. The rarely occurring taxon Platysuchus multiscrobiculatus is anatomically described in detail for the first time. It shows both in the skull and in the postcranial material morphological differences to Steneosaurus bollensis and Pelagosaurus typus. Thus Pl. multiscrobiculatus possesses, e.g., an ilium with a deeper acetabulum and a femur with a distinctly flexed femoral head. A juvenile specimen of Pl. multiscrobiculatus is now discovered and is described in parts for the first time, too. Furthermore, Steneosaurus gracilirostris and Steneosaurus brevior known from Lower Jurassic deposits of England are examined and in parts revised. In this work, Steneosaurs brevior is discovered with one specimen from the Upper Liassic of Holzmaden, Germany for the first time, and provides new evidence for the palaeobiogeographical distribution of the taxon. Because of the high number of investigated specimens, it is possible to study ontogenetic development from juvenile to adult stage in Steneosaurus bollensis, Pelagosaurus typus, and Platysuchus multiscrobiculatus. Biometric data are collected from thalattosuchians and extant crocodilians (e.g. Gavialis gangeticus) to investigate intraspecific variation, ontogenetic development, and taxa differentiation. The skulls of Platysuchus multiscrobiculatus and Steneosaurus bollensis are reconstructed three-dimensionally as wax models. The skull reconstructions form the basis of the jaw muscle restoration of Steneosaurus bollensis in connection with comparative studies at extant crocodilians. By means of functional morphologic analysis of the jaw musculature, the dentition, and the locomotor system of S. bollensis, possible conclusions are drawn for the prey options and the hunting behaviour. To clarify the relationships within the Thalattosuchia, a computer-based cladistic phylogenetic in-group analyse of 25 Thalattosuchia taxa is performed. For the analysis, following Thalattosuchia taxa are studied likewise at original material for comparisons: Metriorhynchus superciliosus, Metriorhynchus hastifer, Metriorhynchus leedsi, Geosaurus gracilis, Geosaurus giganteus, Teleidosaurus calvadosi, Teleidosaurus gaudryi, Teleosaurus cadomensis, Teleosaurus geoffroyi, Steneosaurus priscus, Steneosaurus edwardsi, Steneosaurus heberti, Steneosaurus leedsi, Steneosaurus boutilieri, Steneosaurus megarhinus, Steneosaurus obtusidens, and Machimosaurus hugii. The phylogenetic in-group analyse based on 115 characters, reveals a sister-group relationship of the monophyletic Teleosauridae and monophyletic Metriorhynchidae. Within the groups, some taxa are probably paraphyletic. The taxon Pelagosaurus typus is nested inside the Teleosauridae and not outside or within the Metriorhynchidae, as many authors suggested it so far. Based on these results, a tentative palaeobiogeographical-evolutionary scenario is developed.

Context-dependent interpretation of the conjunction 'und' in different age-groups

In contrast to formal semantics, the conjunction and is nonsymmetrical in pragmatics. The events in Marc went to bed and fell asleep seem to have occurred chronologically although no explicit time reference is given. As the temporal interpretation appears to be weaker in Mia ate chocolate and drank milk, it seems that the kind and nature of events presented in a context influences the interpretation of the conjunction. This work focuses on contextual influences on the interpretation of the German conjunction und (‘and’). A variety of theoretic approaches are concerned with whether and contributes to the establishment of discourse coherence via pragmatic processes or whether the conjunction has complex semantic meaning. These approaches are discussed with respect to how they explain the temporal and additive interpretation of the conjunction and the role of context in the interpre-tation process. It turned out that most theoretic approaches do not consider the importance of different kinds of context in the interpretation process.rnIn experimental pragmatics there are currently only very few studies that investigate the inter-pretation of the conjunction. As there are no studies that investigate contextual influences on the interpretation of und systematically or investigate preschoolers interpretation of the con-junction, research questions such as How do (preschool) children interpret ‘und’? and Does the kind of events conjoined influence children’s and adults’ interpretation? are yet to be answered. Therefore, this dissertation systematically investigates how different types of context influence children’s interpretation of und. Three auditory comprehension studies were conducted in German. Of special interest was whether and how the order of events introduced in a context contributes to the temporal read-ing of the conjunction und. Results indicate that the interpretation of und is – at least in Ger-man – context-dependent: The conjunction is interpreted temporally more often when events that typical occur in a certain order are connected (typical contexts) compared to events with-out typical event order (neutral contexts). This suggests that the type of events conjoined in-fluences the interpretation process. Moreover, older children and adults interpret the conjunc-tion temporally more often than the younger cohorts if the conjoined events typically occur in a certain order. In neutral contexts, additive interpretations increase with age. 5-year-olds reject reversed order statements more often in typical contexts compared to neutral contexts. However, they have more difficulties with reversed order statements in typical contexts where they perform at chance level. This suggests that not only the type of event but also other age-dependent factors such as knowledge about scripts influence children’s performance. The type of event conjoined influences children’s and adults’ interpretation of the conjunction. There-fore, the influence of different event types and script knowledge on the interpretation process does not only have to be considered in future experimental studies on language acquisition and pragmatics but also in experimental pragmatics in general. In linguistic theories, context has to be given a central role and a commonly agreed definition of context that considers the consequences arising from different event types has to be agreed upon.

Periodic Higgs-de Rham flows and representations of algebraic fundamental groups

Let k := bar{F}_p for p > 2, W_n(k) := W(k)/p^n and X_n be a projective smooth W_n(k)-scheme which is W_{n+1}(k)-liftable. For all n > 1, we construct explicitly a functor, which we call the inverse Cartier functor, from a subcategory of Higgs bundles over X_n to a subcategory of flat Bundles over X_n. Then we introduce the notion of periodic Higgs-de Rham flows and show that a periodic Higgs-de Rham flow is equivalent to a Fontaine-Faltings module. Together with a p-adic analogue of Riemann-Hilbert correspondence established by Faltings, we obtain a coarse p-adic Simpson correspondence.