If V is a commutative algebraic group over a field k, O is a commutative ring that acts on V , and I is a finitely generated free O-module with a right action of the absolute Galois group of k, then there is a commutative algebraic group I ⊗O V over k, which is a twist of a power of V . These group varieties have applications to cryptography (in the cases of abelian varieties and algebraic tori...

A Latin square design whose automorphism group is transitive of rank at most 3 on points must come from the multiplication table of an elementary abelian p-group,

1 K and K0 of schemes Let X be a quasi-projective variety. We define K(X) as follows. Let Fvb(X) be the free abelian group on all isomorphism classes of vector bundles (of finite rank) over X and consider the equivalence relation Rvb(X) generated by the following. If 0 → E1 → E2 → E3 → 0 is an exact sequence of vector bundles, then [E2] = [E1] + [E3]. The quotient Fvb(X)/Rvb(X) is called K(X). ...

,Abstract. It is shown that an integrity basis of absolute invariants for any representation of a finite abelian group follows from one integrity basis universal for this group-the typical integrity basis (TIB). An algorithm based 0n.a subsequent multiplication of monomial bases to irreducible representations is found for deriving the TIB. The concept of integrity basis is extended to relative ...

Erdös raised the question whether there exist infinite abelian squarefree words over a given alphabet, that is, words in which no two adjacent subwords are permutations of each other. It can easily be checked that no such word exists over a three-letter alphabet. However, infinite abelian square-free words have been constructed over alphabets of sizes as small as four. In this paper, we investi...

Six-dimensional supergravity theories and their duality properties play a central role in the context of string duality and string compactifications. Lowering dimensions leads usually to an increasing complexity of theories; with this respect six dimensions seem to constitute an appropriate compromise between the physical four and the presumably more fundamental ten or eleven dimensions. In thi...