On some Λ-analytic pro-p groups

This paper is devoted to the first steps towards a systematic study of pro-p groups which are analytic over a commutative Noetherian local pro-p ring Λ, e.g. Λ= . We restrict our attention to Λ-standard groups, which are pro-p groups arising from a formal group defined over Λ. Under some additional assumptions we show that these groups are of ‘intermediate growth’ in various senses, strictly betweenp-adic analytic pro-p groups and free pro-p groups. This suggests a refinement of Lazard's theory which stresses the dichotomy betweenp-adic analytic pro-p groups and all the others. In the course of the discussion we answer a question posed in [LM1], and settle two conjectures from [Bo].     

Discrete groups of slow subgroup growth

It is known that the subgroup growth of finitely generated linear groups is either polynomial or at least $n^{\frac{{\log n}}{{\log \log n}}} $ . In this paper we prove the existence of a finitely generated group whose subgroup growth is of type $n^{\frac{{\log n}}{{(\log \log n)^2 }}} $ . This is the slowest non-polynomial subgroup growth obtained so far for finitely generated groups. The subgroup growth typen ^logn is also realized. The proofs involve analysis of the subgroup structure of finite alternating groups and finite simple groups in general. For example, we show there is an absolute constantc such that, ifT is any finite simple group, thenT has at mostn ^{c logn} subgroups of indexn.     

The length and depth of algebraic groups

Mathematische Zeitschrift - Let G be a connected algebraic group. An unrefinable chain of G is a chain of subgroups $$G = G_0> G_1> \cdots > G_t = 1$$ , where each $$G_i$$ is a...     

Aggregation Mode,Host-Guest Chemistry in Water,and Extraction Capability of an Uncharged,Water-Soluble,Liquid Pillar[5]arene Derivative

An uncharged, water-soluble per-ethylene-glycol pillar[5]arene derivative ( 1 ) was synthesized and its aggregation mode, host-guest chemistry in water and extraction ability was explored. Compound 1 is a liquid at room temperature; in water, limited self-aggregation occurred at high concentrations as deduced from diffusion NMR and dynamic light scattering. Compound 1 forms pseudo-rotaxane-like 1 : 1 host-guest complexes with 1,ω-di-substituted alkanes with association constants on the order of 10³–10⁴ m ⁻¹. Interestingly, NMR experiments showed that the guest location relative to the host ring system differs among the different complexes. In proof-of-concept experiments, compound 1 was shown to extract structurally related organic compounds from benzene into water with significant selectivity. Compound 1 , which is a liquid at room temperature and has only limited interactions with its side arms, can, in principle, be regarded as a complement to or as a kind of type I porous liquid.     

Cannabis-Derived Compounds Cannabichromene and Δ9-Tetrahydrocannabinol Interact and Exhibit Cytotoxic Activity against Urothelial Cell Carcinoma Correlated with Inhibition of Cell Migration and Cytoskeleton Organization

Cannabis sativa contains more than 500 constituents, yet the anticancer properties of the vast majority of cannabis compounds remains unknown. We aimed to identify cannabis compounds and their combinations presenting cytotoxicity against bladder urothelial carcinoma (UC), the most common urinary system cancer. An XTT assay was used to determine cytotoxic activity of C. sativa extracts on T24 and HBT-9 cell lines. Extract chemical content was identified by high-performance liquid chromatography (HPLC). Fluorescence-activated cell sorting (FACS) was used to determine apoptosis and cell cycle, using stained F-actin and nuclei. Scratch and transwell assays were used to determine cell migration and invasion, respectively. Gene expression was determined by quantitative Polymerase chain reaction (PCR). The most active decarboxylated extract fraction (F7) of high-cannabidiol (CBD) C. sativa was found to contain cannabichromene (CBC) and Δ9-tetrahydrocannabinol (THC). Synergistic interaction was demonstrated between CBC + THC whereas cannabinoid receptor (CB) type 1 and type 2 inverse agonists reduced cytotoxic activity. Treatments with CBC + THC or CBD led to cell cycle arrest and cell apoptosis. CBC + THC or CBD treatments inhibited cell migration and affected F-actin integrity. Identification of active plant ingredients (API) from cannabis that induce apoptosis and affect cell migration in UC cell lines forms a basis for pre-clinical trials for UC treatment.     

A Tandem In Situ Peptide Cyclization through Trifluoroacetic Acid Cleavage

We present a new approach for peptide cyclization during solid phase synthesis under highly acidic conditions. Our approach involves simultaneous in situ deprotection, cyclization and trifluoroacetic acid (TFA) cleavage of the peptide, which is achieved by forming an amide bond between a lysine side chain and a succinic acid linker at the peptide N‐terminus. The reaction proceeds via a highly active succinimide intermediate, which was isolated and characterized. The structure of a model cyclic peptide was solved by NMR spectroscopy. Theoretical calculations support the proposed mechanism of cyclization. Our new methodology is applicable for the formation of macrocycles in solid‐phase synthesis of peptides and organic molecules.     

Groups with super-exponential subgroup growth

We show that, if the subgroup growth of a finitely generated (abstract or profinite) groupG is super-exponential, then every finite group occurs as a quotient of a finite index subgroup ofG. The proof involves techniques from finite permutation groups, and depends on the Classification of Finite Simple Groups.The first author was partially supported by the Hungarian National Foundation for Scientific Research, Grant No. T7441. The second author was partially supported by the Israeli National Science Foundation.     

Energy spectra of delayed neutrons from separated fission products: (III). The precursors 88Br, 90Br, 138I, 140I, 142(Xe+Cs) and 144Cs

Energy spectra of delayed neutrons from the mass-separated fission products ^{88. 90}Br, ^{138, 14}I, ¹⁴²(Xe+Cs) and ¹⁴⁴Cs have been measured. Average level spacings, neutron envelopes and P_n values were calculated and compared with the experimental data. The neutron envelopes are well reproduced for all precursors except ⁹⁰Br and ¹⁴⁰I. For the latter the neutron window predicted by various mass formulae is too wide and a considerable reduction was found necessary to bring calculated envelopes in agreement with the experimental distributions.