Normal subgroups and elementary theories of lattice-ordered groups

We show that any lattice-ordered group (l-group) G can be l-embedded into continuously many l-groups H _i which are pairwise elementarily inequivalent both as groups and as lattices with constant e. Our groups H _i can be distinguished by group-theoretical first-order properties which are induced by lattice-theoretically nice properties of their normal subgroup lattices. Moreover, they can be taken to be 2-transitive automorphism groups A(S _i ) of infinite linearly ordered sets (S _i , ) such that each group A(S _i ) has only inner automorphisms. We also show that any countable l-group G can be l-embedded into a countable l-group H whose normal subgroup lattice is isomorphic to the lattice of all ideals of the countable dense Boolean algebra B.     

Durch Bromierung ausgelöste Umlagerung tertiärer Allylalkohole: Der Einfluss eines Fluor-Substituenten auf Reaktionsgeschwindigkeit und Reaktionsverlauf

Rearrangement of Tertiary Allyl Alcohols Induced by Bromination: The Effect of a Fluorine Substituent on the Rate and the Outcome of the Reaction The allyl alcohol bearing a methyl and a t-butyl group at the hydroxylated position was found to undergo a rearrangement when treated with bromine (or N-bromosuccinimide) in an aqueous medium and to afford a product mixture containing two regioisomeric ketones and one oxirane. Introduction of an additional methyl group or a fluorine atom at the non-terminal olefinic center led to a more selective discrimination between potential migratory groups. As the result of an exclusive t-butyl shift only one product, a ketone, was formed in both cases. Whereas the reaction rate was only slightly affected by the additional methyl group, it was substantially decreased by the fluorine atom.