Characterization of classical groups by orbit sizes on the natural module

We show that if is a finite vector space, and is a subgroup of having the same orbit sizes on 1-spaces as an orthogonal or unitary group on , then, with a few exceptions, is itself an orthogonal or unitary group on .

     

Labelings of two classes of plane graphs

The paper describes magic labelings of type (1,1,1) for two classes of graphs, which are obtained by a combination of vertex, edge and face labelings.     

On the Claisen Rearrangement of Allyl Ethyl Ketene Acetals Generated in situ via Benzeneselenenic Acid Eliminiation

Mixed acetals 7 of benzeneseleninylacetaldehyde, prepared by a simple 2-step procedure from mono- and bicyclic allylic alcohols 5 , undergo benzeneselenenic acid elimination to transient ketene acetals 8 which afford γ, δ-unsaturated esters 9 via the ester Claisen rearrangement (Scheme 2). Under the same conditions selenoxide 7h derived from benzyl alcohol 5h is converted back to benzyl alcohol with the concomitant formation of ethylphenylselenoacetate 12 .