Related papers: Abelian powers in paper-folding words

In this paper we find a necessary and sufficient condition for a finite nilpotent group to have an abelian central automorphism group.

It is proved that any infinite Abelian group of infinite exponent admits a non-discrete reflexive group topology.

Let p be a fixed prime. An Abelian p-group is an Abelian group (not necessarily finitely generated) in which every element has for its order some power of p. The countable Abelian p-groups are classified by Ulm's theorem, and Khisamiev…

In this paper, we prove the existence of certain lifts of Hilbert cusp forms to general odd spin groups. We then use those lifts to provide evidence for a conjecture of Gross on the modularity of abelian varieties not of ${\rm GL}_2$-type.

In this paper we begin the systematic study of group equations with abelian predicates in the main classes of groups where solving equations is possible. We extend the line of work on word equations with length constraints, and more…

In this paper, we classify the possible group structures on the set of $R$-valued points of an abelian variety, where $R$ is any real closed field. We make use of a family of abelian varieties that, in effect, allows one to quantify over…

We study the following problem, first introduced by Dekking. Consider an infinite word x over an alphabet {0,1,...,k-1} and a semigroup homomorphism S:{0,1,...,k-1}* -> N. Let L_x denote the set of factors of x. What conditions on S and the…

We study Calabi-Yau threefolds fibered by abelian surfaces, in particular, their arithmetic properties, e.g., N\'eron models and Zariski density.

In this paper we introduce and study a family of complexity functions of infinite words indexed by $k \in \ints ^+ \cup {+\infty}.$ Let $k \in \ints ^+ \cup {+\infty}$ and $A$ be a finite non-empty set. Two finite words $u$ and $v$ in $A^*$…

We give an accessible and modern description of the automorphisms of a finite abelian group $G$. Included is an explicit formula for the cardinality of $Aut(G)$.

In the paper we prove for every finite algebra A that either it has the polynomially generated powers (PGP) property, or it has the exponentially generated powers (EGP) property. For idempotent algebras we give a simple criteria for the…

Two interleaved phonebooks are nearly impossible to separate by pulling their spines. The very slight force exerted by the outer sheets of the assembly is amplified as the exponential of the square of the number of sheets, leading to a…

We show that infinitesimal Torelli for $n$-forms holds for abelian covers of algebraic varieties of dimension $n\ge 2$, under some explicit ampleness assumptions on the building data of the cover. Moreover, we prove a variational Torelli…

In this note we give a theoretical support by means of quotient polynomial rings for the computation formulas of the dimension of abelian codes.

We show that the first-order logical theory of the binary overlap-free words (and, more generally, the ${\alpha}$-free words for rational ${\alpha}$, $2 < {\alpha} \leq 7/3$), is decidable. As a consequence, many results previously obtained…

In this paper, we consider infinite words that arise as fixed points of primitive substitutions on a finite alphabet and finite colorings of their factors. Any such infinite word exhibits a "hierarchal structure" that will allow us to…

Following Inoue et al., we define a word to be a repetition if it is a (fractional) power of exponent at least 2. A word has a repetition factorization if it is the product of repetitions. We study repetition factorizations in several…

We determine which complex abelian varieties can be realized as the automorphism group of a smooth projective variety.

We introduce a {\it non-regular} generalisation of the N\"{o}rlund mean, and show its equivalence with a certain moving average. The Abelian and Tauberian theorems establish relations with convergent sequences and certain power series. A…

We construct words with small image in a given finite alternating or unimodular group. This shows that word width in these groups is unbounded in general.