Factorizations of finite groups by conjugate subgroups which are solvable or nilpotent

We consider factorizations of a finite group $G$ into conjugate subgroups, $G=A^{x_{1}}\cdots A^{x_{k}}$ for $A\leq G$ and $x_{1},\ldots ,x_{k}\in G$, where $A$ is nilpotent or solvable. First we exploit the split $BN$-pair structure of finite simple groups of Lie type to give a unified self-contained proof that every such group is a product of four or three unipotent Sylow subgroups. Then we derive an upper bound on the minimal length of a solvable conjugate factorization of a general finite group. Finally, using conjugate factorizations of a general finite solvable group by any of its Carter subgroups, we obtain an upper bound on the minimal length of a nilpotent conjugate factorization of a general finite group

Higher Dosage of the Epidermal Growth Factor Receptor Mutant Allele in Lung Adenocarcinoma Correlates with Younger Age, Stage IV at Presentation, and Poorer Survival

IntroductionThe clinical significance of epidermal growth factor receptor (EGFR) mutant allele specific imbalance (MASI) in lung adenocarcinomas is unknown.MethodsEGFR MASI was characterized by sequencing electropherograms (SEs) and EGFR fluorescence in situ hybridization (FISH) in 96 prospectively tested lung adenocarcinoma patients with a median follow-up of 20 months (all cases were EGFR mutation-positive).ResultsIn 25 cases, the mutant allele (MA) peak was higher than the wild-type allele (WA) peak, indicating the presence of EGFR MASI (25/96, 26%). The adenocarcinomas with EGFR MASI had a 4.4-fold higher average EGFR/Chromosome Enumeration Probe 7 ratio than carcinomas without MASI (7.9 ± 3.8 versus 1.8 ± 0.6, p = 0.01). A high degree of correlation between the MA/WA ratio (SE) and the EGFR/CEP7 ratio (FISH) (ρ = 0.757, p = 0.003) validated the quantitative nature of SE. Amplification was the most common mechanism of EGFR MASI (13/21, 62%). EGFR MASI was more commonly associated with exon 19 mutations than with exon 21 mutations (19/53, 36%, versus 6/43, 14%, p = 0.015, odds ratio [OR] = 3.4) and in patients younger than 65 years (17/46, 37%, versus 8/50, 16%, p = 0.019, OR = 3.1). Patients with EGFR MASI presented with stage IV disease more frequently (p = 0.01, OR = 3.5) and had a poorer disease-specific survival rate (p = 0.021, 54% versus 83% at 31 months).ConclusionsEGFR MASI in lung adenocarcinomas can be assessed based on SE and can be used to identify younger patients with more aggressive disease

Spin phase diagram of the nu_e=4/11 composite fermion liquid

Spin polarization of the "second generation" nu_e=4/11 fractional quantum Hall state (corresponding to an incompressible liquid in a one-third-filled composite fermion Landau level) is studied by exact diagonalization. Spin phase diagram is determined for GaAs structures of different width and electron concentration. Transition between the polarized and partially unpolarized states with distinct composite fermion correlations is predicted for realistic parameters.Comment: 5 pages, 3 figure

On Hoelder-continuity of Oseledets subspaces

29 pages; corrected a few typos and added several references and comments following referee suggestions (this is the final version content to appear in JLMS)International audienceFor Hoelder cocycles over a Lipschitz base transformation, possibly non-invertible, we show that the subbundles given by the Oseledets Theorem are Hoelder-continuous on compact sets of measure arbitrarily close to 1. The results extend to vector bundle automorphisms, as well as to the Kontsevich-Zorich cocycle over the Teichmueller flow on the moduli space of abelian differentials. Following a recent result of Chaika-Eskin, our results also extend to any given Teichmueller disk

In vitro FRAP reveals the ATP-dependent nuclear mobilization of the exon junction complex protein SRm160

We present a new in vitro system for characterizing the binding and mobility of enhanced green fluorescent protein (EGFP)-labeled nuclear proteins by fluorescence recovery after photobleaching in digitonin-permeabilized cells. This assay reveals that SRm160, a splicing coactivator and component of the exon junction complex (EJC) involved in RNA export, has an adenosine triphosphate (ATP)-dependent mobility. Endogenous SRm160, lacking the EGFP moiety, could also be released from sites at splicing speckled domains by an ATP-dependent mechanism. A second EJC protein, RNPS1, also has an ATP-dependent mobility, but SRm300, a protein that binds to SRm160 and participates with it in RNA splicing, remains immobile after ATP supplementation. This finding suggests that SRm160-containing RNA export, but not splicing, complexes have an ATP-dependent mobility. We propose that RNA export complexes have an ATP-regulated mechanism for release from binding sites at splicing speckled domains. In vitro fluorescence recovery after photobleaching is a powerful tool for identifying cofactors required for nuclear binding and mobility