Representations of the Gupta-Sidki group

If is an odd prime, then the Gupta-Sidki group is an infinite -generated -group. It is defined in a recursive manner as a particular subgroup of the automorphism group of a regular tree of degree . In this note, we make two observations concerning the irreducible representations of the group algebra with an algebraically closed field. First, when , we obtain a lower bound for the number of irreducible representations of any finite degree . Second, when , we show that if has one nonprincipal irreducible representation, then it has infinitely many. The proofs of these two results use similar techniques and eventually depend on the fact that the commutator subgroup of has a normal subgroup of finite index isomorphic to the direct product of copies of .

     

A unique reversal of elution order during direct enantiomeric resolution of amide derivatives of 1-phenyl-2-aminopropane by high performance liquid chromatography on chiral stationary phases

Enantiomeric amide derivatives of (S)- and (R)-1-phenyl-2-aminopropane (dextro- and levoamphetamine, respectively) were resolved by high performance liquid chromatography on commercially available ionically and covalently bonded chiral stationary phases ((R)-N-(3,5-dinitrobenzoyl)phenylglycine). Ten enantiomeric amide pairs were synthesized and chromatographed on the columns by using a mobile phase of hexane-isopropanol (97 : 3), a flow rate of 2 ml/min, and a column temperature of 20°C. The (R)-isomer of all 10 amides eluted first on the covalent column as did the (R)-isomer of nine derivatives on the ionic column. however, the 3,5-dinitrobenzoyl amide of (S)- amphetamine eluted before the (R)-isomer on the ionic column. This reversal in enantiomeric elution order reveals the complexity of the interactions occurring on these columns and emphasizes the hazards of relying on observed elution order as an a priori indication of absolute configuration.     

Applied potential and radiotracer studies on poly(vinyl chloride) matrix ion-selective electrode membranes

This paper reports the effect of applied potentials on PVC matrix membranes containing (i) the barium ion-sensitive barium-Antarox C0880 complex and 2-nitrophenyl phenyl ether solvent mediator, and (ii) the calcium ion-sensitive Orion 92-20-02 phosphate-based calcium liquid ion-exchanger. Platinum electrodes were placed in solutions on each side of the membranes. The barium ion-sensitive membranes are unable to maintain stable current flows but the calcium ion-sensitive membranes are characterized by stable current flows over prolonged periods even after successive polarity reversals. Results are presented, from radiotracer experiments for permeation of ions through the membranes with and without an applied potential. No evidence was found for significant permeation of barium-133 ions through the barium ion-sensing membranes into an initially inactive solution, but it was found that barium-133 ions were incorporated into the membranes after removal of the applied potential. Permeation of sodium-22 ions through the calcium ion-sensing membranes occurred only to a limited extent in the presence of an applied potential and not at all in its absence, confirming electrode selectivity trends for calcium and sodium. Calcium-45 ions did not permeate the calcium ion-sensing membranes into an inactive counter-solution against the potential gradient, but on reversal of the polarity, permeation occurred to a far greater extent than in the absence of an applied potential. These differences in behaviour are compatible with the more complicated membrane pathways of the barium ion-sensing membranes, imposed by the complexing of barium ions by the ethyleneoxy units of Antarox C0880 in a tight helical conformation. The calcium ion-sensing membranes are much less constrained, thus permitting more facile replacement of the calcium ions in the membrane by ions from solution.     

Derivatives of 2,4-diamino-6-methylpteridine

Eighteen derivatives of 2,4-diamino-6-methylpteridine related to methotrexate and aminopterin have been prepared from 6-(bromomethyl)-2,4-pteridinediamine by nucleophilic displacement reactions. None of these compounds showed any antileukemic acitivity.     

Steric selectivity in oxidations of diols

Oxidations of 2,2-disubstituted-1,4-butanediols by the combination of nickel(II) bromide and benzoyl peroxide and by trityl tetrafluoroborate produce β,β-disubstituted-γ-butyrolactones with exceptional selectivity.     

Rh(II)-Catalyzed Isomerizations of Cyclopropenes Evidence for Rh(II)-Complexed Vinylcarbene Intermediates

The thermocatalytic rearrangements of cyclopropenes 1-4 have been investigated in the presence of Rh(IT) perfiuorobutyrate. 1, 2, 3-Triphenylcyclopropene ( 1a ) undergoes rearrangement lo diphenylindene 5a or, with alkoxycyclopropene derivatives, to α, β-unsaturated ketone 6. Furan formation occurs with 2, 3-diphenylcyclo-propenecarboxylate 2, but the diethyl counterpart 3 rearranges to dienoate 8. 2-Alkylcyclopropenecarboxylates 4 afforded (E)-methylidenecyclopentane derivatives 9 as the only isolable product in yields of ca. 35 %. A mechanism involving regio- and stereospecific cyclopropene ring opening to a Rh-complexed vinylcarbene and insertion of the latter into the C? H bond to give 9 is proposed. An analogous mechanism should account for the rearrangement products of 1 to 3 .     

Methylation and amination of folic acid

The methylation of folic acid (2) with excess methyl iodide resulted in the formation of dimethyl 1,3-dimethylfolate ( 4 ), whereas, methylation of dimethyl folate ( 3 ) with an equimolar amount of methyl iodide gave mainly dimethyl 3-methylfolate ( 6 ). Both 4 and 6 underwent the Dimroth rearrangement in base to give the corresponding 2-deamino-2-methyiamino folic acids 5 and 7, respectively. Amination of 2 with hydroxylamine-O-sulfonic acid in dilute base gave a low yield of 3-amino folic acid (8), which underwent Dimroth rearrangement to give 2-deamino-2-hydrazino folic acid (9) in an acidic, but not a basic, medium.