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.

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.

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.

A river runs through it - ancient DNA data on the neolithic populations of the Great Hungarian Plain

This thesis was part of a multidisciplinary research project funded by the German Research Foundation (“Bevölkerungsgeschichte des Karpatenbeckens in der Jungsteinzeit und ihr Einfluss auf die Besiedlung Mitteleuropas”, grant no. Al 287/10-1) aimed at elucidating the population history of the Carpathian Basin during the Neolithic. The Carpathian Basin was an important waypoint on the spread of the Neolithic from southeastern to central Europe. On the Great Hungarian Plain (Alföld), the first farming communities appeared around 6000 cal BC. They belonged to the Körös culture, which derived from the Starčevo-Körös-Criş complex in the northern Balkans. Around 5600 cal BC the Alföld-Linearbandkeramik (ALBK), so called due to its stylistic similarities with the Transdanubian and central European LBK, emerged in the northwestern Alföld. Following a short “classical phase”, the ALBK split into several regional subgroups during its later stages, but did not expand beyond the Great Hungarian Plain. Marking the beginning of the late Neolithic period, the Tisza culture first appeared in the southern Alföld around 5000 cal BC and subsequently spread into the central and northern Alföld. Together with the Herpály and Csőszhalom groups it was an integral part of the late Neolithic cultural landscape of the Alföld. Up until now, the Neolithic cultural succession on the Alföld has been almost exclusively studied from an archaeological point of view, while very little is known about the population genetic processes during this time period. The aim of this thesis was to perform ancient DNA (aDNA) analyses on human samples from the Alföld Neolithic and analyse the resulting mitochondrial population data to address the following questions: is there population continuity between the Central European Mesolithic hunter-gatherer metapopulation and the first farming communities on the Alföld? Is there genetic continuity from the early to the late Neolithic? Are there genetic as well as cultural differences between the regional groups of the ALBK? Additionally, the relationships between the Alföld and the neighbouring Transdanubian Neolithic as well as other European early farming communities were evaluated to gain insights into the genetic affinities of the Alföld Neolithic in a larger geographic context. 320 individuals were analysed for this study; reproducible mitochondrial haplogroup information (HVS-I and/or SNP data) could be obtained from 242 Neolithic individuals. According to the analyses, population continuity between hunter-gatherers and the Neolithic cultures of the Alföld can be excluded at any stage of the Neolithic. In contrast, there is strong evidence for population continuity from the early to the late Neolithic. All cultural groups on the Alföld were heavily shaped by the genetic substrate introduced into the Carpathian Basin during the early Neolithic by the Körös and Starčevo cultures. Accordingly, genetic differentiation between regional groups of the ALBK is not very pronounced. The Alföld cultures are furthermore genetically highly similar to the Transdanubian Neolithic cultures, probably due to common ancestry. In the wider European context, the Alföld Neolithic cultures also highly similar to the central European LBK, while they differ markedly from contemporaneous populations of the Iberian Peninsula and the Ukraine. Thus, the Körös culture, the ALBK and the Tisza culture can be regarded as part of a “genetic continuum” that links the Neolithic Carpathian Basin to central Europe and likely has its roots in the Starčevo -Körös-Criş complex of the northern Balkans.