Growth in solvable subgroups of GL_r(Z/pZ)

Let $K=Z/pZ$ and let $A$ be a subset of \GL_r(K) such that is solvable. We reduce the study of the growth of $A$ under the group operation to the nilpotent setting. Specifically we prove that either $A$ grows rapidly (meaning $|A\cdot A\cdot A|\gg |A|^{1+\delta}$), or else there are groups $U_R$ and $S$, with $S/U_R$ nilpotent such that $A_k\cap S$ is large and $U_R\subseteq A_k$, where $k$ is a bounded integer and $A_k = \{x_1 x_2...b x_k : x_i \in A \cup A^{-1} \cup {1}}$. The implied constants depend only on the rank $r$ of $\GL_r(K)$. When combined with recent work by Pyber and Szab\'o, the main result of this paper implies that it is possible to draw the same conclusions without supposing that is solvable.Comment: 46 pages. This version includes revisions recommended by an anonymous referee including, in particular, the statement of a new theorem, Theorem

On normalish subgroups of the R. Thompson groups

Funding: UK EPSRC grant EP/R032866/1Results in C∗ algebras, of Matte Bon and Le Boudec, and of Haagerup and Olesen, apply to the R. Thompson groups F ≤ T ≤ V. These results together show that F is non-amenable if and only if T has a simple reduced C∗-algebra. In further investigations into the structure of C∗-algebras, Breuillard, Kalantar, Kennedy, and Ozawa introduce the notion of a normalish subgroup of a group G. They show that if a group G admits no non-trivial finite normal subgroups and no normalish amenable subgroups then it has a simple reduced C∗-algebra. Our chief result concerns the R. Thompson groups F < T < V; we show that there is an elementary amenable group E < F (where here, E ≅ ...)≀Z)≀Z)≀Z) with E normalish in V. The proof given uses a natural partial action of the group V on a regular language determined by a synchronizing automaton in order to verify a certain stability condition: once again highlighting the existence of interesting intersections of the theory of V with various forms of formal language theory.Postprin

Small doubling in groups

Let A be a subset of a group G = (G,.). We will survey the theory of sets A with the property that |A.A| <= K|A|, where A.A = {a_1 a_2 : a_1, a_2 in A}. The case G = (Z,+) is the famous Freiman--Ruzsa theorem.Comment: 23 pages, survey article submitted to Proceedings of the Erdos Centenary conferenc

Compactifications and algebraic completions of Limit groups

In this paper we consider the existence of dense embeddings of Limit groups in locally compact groups generalizing earlier work of Breuillard, Gelander, Souto and Storm [GBSS] where surface groups were considered. Our main results are proved in the context of compact groups and algebraic groups over local fields. In addition we prove a generalization of the classical Baumslag lemma which is a useful tool for generating eventually faithful sequences of homomorphisms. The last section is dedicated to correct a mistake from [BGSS] and to get rid of the even genus assumption.Comment: v2: Substantial changes to sections 7 and 8.2. Typos corrected. References added. v3: Acknowledgement correcte

European Sea Bass (Dicentrarchus labrax) immune status and disease resistance are impaired by arginine dietary supplementation

Infectious diseases and fish feeds management are probably the major expenses in the aquaculture business. Hence, it is a priority to define sustainable strategies which simultaneously avoid therapeutic procedures and reinforce fish immunity. Currently, one preferred approach is the use of immunostimulants which can be supplemented to the fish diets. Arginine is a versatile amino acid with important mechanisms closely related to the immune response. Aiming at finding out how arginine affects the innate immune status or improve disease resistance of European seabass (Dicentrarchus labrax) against vibriosis, fish were fed two arginine-supplemented diets (1% and 2% arginine supplementation). A third diet meeting arginine requirement level for seabass served as control diet. Following 15 or 29 days of feeding, fish were sampled for blood, spleen and gut to assess cell-mediated immune parameters and immune-related gene expression. At the same time, fish from each dietary group were challenged against Vibrio anguillarum and survival was monitored. Cell-mediated immune parameters such as the extracellular superoxide and nitric oxide decreased in fish fed arginine-supplemented diets. Interleukins and immune-cell marker transcripts were down-regulated by the highest supplementation level. Disease resistance data were in accordance with a generally depressed immune status, with increased susceptibility to vibriosis in fish fed arginine supplemented diets. Altogether, these results suggest a general inhibitory effect of arginine on the immune defences and disease resistance of European seabass. Still, further research will certainly clarify arginine immunomodulation pathways thereby allowing the validation of its potential as a prophylactic strategy.European Union's Seventh Framework Programme AQUAEXCEL (Aquaculture Infrastructures for Excellence in European Fish Research) [262336]; AQUAIMPROV [NORTE-07-0124-FEDER-000038]; North Portugal Regional Operational Programme (ON. 2 - O Novo Norte) , under the National Strategic Reference Framework, through the European Regional Development Fund; North Portugal Regional Operational Programme (ON. 2 - O Novo Norte), under the National Strategic Reference Framework through the COMPETE - Operational Competitiveness Programme; Fundacao para a Ciencia e Tecnologia; Fundacao para a Ciencia e Tecnologia [SFRH/BD/89457/2012, SFRH/BPD/77210/2011]; Generalitat Valenciana through the project REVIDPAQUA [ISIC/2012/003]; [PEst-C/MAR/LA0015/2013]; [UID/Multi/04423/2013]info:eu-repo/semantics/publishedVersio

C*-simplicity and the unique trace property for discrete groups

In this paper, we introduce new methods for working with group and crossed product C*-algebras that allow us to settle the longstanding open problem of characterizing groups with the unique trace property

Model theory of finite and pseudofinite groups

This is a survey, intended both for group theorists and model theorists, concerning the structure of pseudofinite groups, that is, infinite models of the first-order theory of finite groups. The focus is on concepts from stability theory and generalisations in the context of pseudofinite groups, and on the information this might provide for finite group theory

Multiscale Systems, Homogenization, and Rough Paths:VAR75 2016: Probability and Analysis in Interacting Physical Systems

In recent years, substantial progress was made towards understanding convergence of fast-slow deterministic systems to stochastic differential equations. In contrast to more classical approaches, the assumptions on the fast flow are very mild. We survey the origins of this theory and then revisit and improve the analysis of Kelly-Melbourne [Ann. Probab. Volume 44, Number 1 (2016), 479-520], taking into account recent progress in $p$-variation and c\`adl\`ag rough path theory.Comment: 27 pages. Minor corrections. To appear in Proceedings of the Conference in Honor of the 75th Birthday of S.R.S. Varadha

Lower-hybrid drift waves and electromagnetic electron space-phase holes associated with dipolarization fronts and field-aligned currents observed by the Magnetospheric Multiscale mission during a substorm

We analyse two ion scale dipolarization fronts associated with field-aligned currents detected by the Magnetospheric Multiscale mission during a large substorm on August 10, 2016. The first event corresponds to a fast dawnward flow with an anti-parallel current and could be generated by the wake of a previous fast earthward flow. It is associated with intense lower-hybrid drift waves detected at the front and propagating dawnward with a perpendicular phase speed close to the electric drift and the ion thermal velocity. The second event corresponds to a flow reversal: from southwward/dawnward to northward/duskward associated with a parallel current consistent with a brief expansion of the plasma sheet before the front crossing, and with a smaller lower-hybrid drift wave activity. Electromagnetic electron phase-space holes are detected near these low-frequency drift waves during both events. The drift waves could accelerate electrons parallel to the magnetic field and produce the parallel electron drift needed to generate the electron holes. Yet, we cannot rule out the possibility that the drift waves are produced by the anti-parallel current associated with the fast flows, leaving the source for the electron holes unexplained