Kaplansky’s “infinite abelian groups” and its two test problems

Abstract

Kaplansky’s Infinite Abelian Groups, originally published in 1954, has recently been republished. In recognition of its continuing significance after 65?years, the authors illustrate some important ideas and techniques described in the book. In particular, a class of groups is defined for which there are affirmative answers to the author’s two famous “Test Problems.”     

Electrospray ionization enters the final frontier: Mass spectrometry's role in understanding electrospray thrusters and their plumes

Electrospray thrusters using ionic liquid (IL)‐based propellants are quickly gaining popularity in spacecraft design. Mass spectrometry is especially well‐suited to provide important knowledge on the fundamentals of how these systems work and on evaluating their efficiencies and impacts, given that the operating principles of electrospray thrusters closely mimics the mass spectrometry experiment – in both ions are generated by electrospray and then enter a vacuum. Here, electrospray thruster technology and IL‐based propellants are briefly introduced. This introduction is then followed by a discussion of mass spectrometry's current contribution to the study of IL‐based electrospray thrusters – with a focus on electrospray, dissociation, and spectroscopy studies – and a brief discussion of areas ripe for immediate contributions from the mass spectrometry community.     

β-Ketoiminato Iridium(III) Organometallic Complexes: Selective Cytotoxicity towards Colorectal Cancer Cells HCT116 p53-/-

This report presents a new library of organometallic iridium(III) compounds of the type [Cp*IrCl(L)] (Cp*=pentamethylcyclopentadienyl and L=a functionalized β-ketoiminato ligand) showing moderate to high cytotoxicity against a range of cancer cell lines. All compounds show increased activity towards colorectal cancer, with preferential activity observed against the immortalized p53-null colorectal cell line, HCT116 p53-/-, with sensitivity factors (SF) up to 26.7. Additionally, the compounds have excellent selectivity for cancerous cells when tested against normal cell types, with selectivity ratios (SR) up to 35.6, contrary to that of cisplatin, which is neither selective nor specific for cancerous cells (SF=0.43 and SR=0.7–2.3). This work provides a preliminary understanding of the cytotoxicity of iridium compounds in the absence of p53 and has potential applications in treatment of cancers for which the p53 gene is absent or mutant.     

Three‐Dimensional Metal–Fullerene Frameworks

Hexakis‐substituted [60]fullerene adducts with icosahedral symmetry provide an unprecedented scaffold for the spatial arrangement of twelve functional groups with high geometric precision. This unique molecular symmetry identifies such polyfunctional organic building blocks as potential highly connective linkers for coordination polymer and metal–organic framework synthesis. Hereby, the linker exhibits a higher connectivity than the metal ions and with the main connectivity based on the ligand, this can create a new type of inversely cross‐linked framework. Two hexakis adducts bearing either twelve glycolic acid or 3‐hydroxypropionic acid side chains attached to its malonate units were incorporated as organic connectivity centers in the first fullerene‐containing three‐dimensional frameworks by coordination with Zn²⁺.     

On Copper(I) Fluorides,the Cuprophilic Interaction,the Preparation of Copper Nitride at Room Temperature,and the Formation Mechanism at Elevated Temperatures

Our attempts to synthesize the hitherto unknown binary copper(I) fluoride have led to first successes and a serendipitious result: By conproportionation of elemental copper and copper(II) fluoride in anhydrous liquid ammonia, two copper(I) fluorides were obtained as simple NH₃ complexes. One of them presents an example of ligand‐unsupported “cuprophilic” interactions in an infinite [Cu₂(NH₃)₄]²⁺ chain with alternating Cu–Cu distances. We discovered that both copper(I) fluorides can easily be converted into Cu₃N at room temperature, just by applying a vacuum. Additionally, we investigated the formation mechanism of the classical synthesis route of Cu₃N that starts with CuF₂ and flowing NH₃ in the temperature range between ambient and 290 °C by means of thermal analysis and in situ neutron diffraction. The reaction proceeds at elevated temperatures through the formation of a blue and amorphous ammoniate Cu(NH₃)₂F₂, the reformation of CuF₂, and finally the redox reaction to form Cu₃N.