A conjecture of M. J. Taylor concerning determinantal congruences

Let G be a finite group. The class group of the group ring of G is a quotient of the idèlic homomorphisms of R(G) by the global functions and the determinantal functions. Using Explicit Brauer Induction, we prove Adams operations, applied to determinantal functions, satisfy some congruences which were conjectured by M. J. Taylor. As an application, we construct some new maps defined on the class group.In memory of J. Frank Adams (1930–1989)Research partially supported by NSERC Grant # 0GP0042580.     

Oxygen capture by lithiated organozinc reagents containing aromatic 2-pyridylamide ligands

The sequential reaction of ZnMe2 with a 2-pyridylamine (HN(2-C5H4N)R, R = Ph: 1; 3,5-Xy (=3,5-xylyl): 2; 2,6-Xy: 3; Bz (=benzyl): 4; Me: 5), tBuLi and thereafter with oxygen affords various lithium zincate species, the solid-state structures of which reveal a diversity of oxo-capture modes. Amine 1 reacts to give both dimeric THF [Li(Me)OZn[N(2-C5H4N)Ph]2] (6), wherein oxygen has inserted into the Zn-C bond of a [MeZn[N(2-C5H4N)-Ph]2] ion, and the trigonal Li2Zn complex, bis(OtBu)-capped (THF x Li)2-[[(mu3-O)tBu]2Zn[N(2-C5H4N)Ph]2] (7). The structural analogue of 6 (8) results from the employment of 2, while the use of more sterically congested 3 yields a pseudo-cubane dimer [(THF x [Li(tBu)OZn(OtBu)Me]]2] (9) notable for the retention of labile Zn-C(Me). Amines 4 and 5 afford the oxo-encapsulation products [mu4-O)Zn4[(2-C5H4N)-NBz]6] (10b), and [tBu(mu3-O)-Li3(mu6-O)Zn3[(2-C5H4N)NMe]6] (11), respectively, with concomitant oxo-insertion into a Li-C interaction resulting in capping of the fac-isomeric (mu6-O)M3M'3 distorted octahedral core of the latter complex by a tert-butoxide group.     

Synthesis of 3-substituted 4-piperidinones via a one-pot tandem oxidation-cyclization-oxidation process: stereodivergent reduction to 3,4-disubstituted piperidines

A novel approach to 3-substituted 4-piperidinones is described. The one-pot tandem oxidation-cyclization-oxidation of unsaturated alcohols 1a-e by PCC or PCC and trifluoromethanesulfonic acid affords piperidinones 2a-e in good yield. Reduction of 2a-e by L-Selectride gives the corresponding cis 3,4-disubstituted piperidines with diastereomeric ratios of >99:1. By contrast, reduction of 2a-e by Al-isopropoxydiisobutylalane gives the trans products with diastereomeric ratios of up to 99:1.