Related papers: Characterizing abelian admissible groups

We characterise the virtually abelian groups which are fundamental groups of compact K\"ahler manifolds and of smooth projective varieties. We show that a virtually abelian group is K\"ahler if and only if it is projective. In particular,…

We make a start on one of George McNulty's Dozen Easy Problems: "Which finite automatic algebras are dualizable?" We give some necessary and some sufficient conditions for dualizability. For example, we prove that a finite automatic algebra…

In this paper, we present new necessary and sufficient conditions under which the sum of two group invertible elements in a Banach algebra has group inverse. We then apply these results to block operator matrices over Banach spaces. The…

As an improvement of the combinatorial realization of totally positive matrices via the essential positive weightings of certain planar network by S.Fomin and A.Zelevisky \cite{[4]}, in this paper, we give the test method of positive…

A group $G$ is called to be acceptable (due to M. Larsen) if for any finite group $H$, two element-conjugate homomorphisms are globally conjugate. We answer the acceptability question for general linear, special linear, unitary, symplectic…

If for all $a, b$ in a group $G$, we have that $a^2b^2 = b^2a^2$ and $a^3b^3 = b^3a^3$ then does the group necessarily have to be abelian? This paper shows that the answer is affirmative for finite groups as well as certain classes of…

Metabelian algebras are introduced and it is shown that an algebra $A$ is metabelian if and only if $A$ is a nilpotent algebra having the index of nilpotency at most $3$, i.e. $x y z t = 0$, for all $x$, $y$, $z$, $t \in A$. We prove that…

Let $A$ be an abelian variety over an algebraically closed field. We show that $A$ is the automorphism group scheme of some smooth projective variety if and only if $A$ has only finitely many automorphisms as an algebraic group. This…

We study amenability of affine algebras (based on the notion of almost-invariant finite-dimensional subspace), and apply it to algebras associated with finitely generated groups. We show that a group G is amenable if and only if its group…

A subset of an abelian group is {\em sequenceable} if there is an ordering $(x_1, \ldots, x_k)$ of its elements such that the partial sums $(y_0, y_1, \ldots, y_k)$, given by $y_0 = 0$ and $y_i = \sum_{j=1}^i x_i$ for $1 \leq i \leq k$, are…

Binary Parseval frames share many structural properties with real and complex ones. On the other hand, there are subtle differences, for example that the Gramian of a binary Parseval frame is characterized as a symmetric idempotent whose…

A set of quasi-uniform random variables $X_1,...,X_n$ may be generated from a finite group $G$ and $n$ of its subgroups, with the corresponding entropic vector depending on the subgroup structure of $G$. It is known that the set of entropic…

We consider the conjugation-action of an arbitrary upper-block parabolic subgroup of the general linear group on the variety of nilpotent matrices in its Lie algebra. Lie-theoretically, it is natural to wonder about the number of orbits of…

We study the interaction between the group law on an abelian variety and the additive structure induced on its image under a morphism to projective space. Let $A/F$ be a simple abelian variety, $f:A \rightarrow \mathbb{P}^n$ be a morphism…

Subsets of a matrix algebra over a field that are invariant under conjugation and contain the linear span of each two of their commuting elements are described. They obviously include the subsets of diagonalizable and nilpotent matrices. In…

We study admissibility of inference rules and unification with parameters in transitive modal logics (extensions of K4), in particular we generalize various results on parameter-free admissibility and unification to the setting with…

We show that every locally compact strictly convex metric group is abelian, thus answering one problem posed by the authors in their earlir paper. To prove this theorem we first construct the isomorphic embeddings of the real line into the…

An endomorphisms $\varphi$ of an abelian group $A$ is said inertial if each subgroup $H$ of $A$ has finite index in $H+\varphi (H)$. We study the ring of inertial endomorphisms of an abelian group. Here we obtain a satisfactory description…

An element of a group is \emph{reversible} if it is conjugate to its own inverse, and it is \emph{strongly reversible} if it is conjugate to its inverse by an involution. A group element is strongly reversible if and only if it can be…

A dimension group is an ordered abelian group that is an inductive limit of a sequence of simplicial groups, and a stationary dimension group is such an inductive limit in which the homomorphism is the same at every stage. If a simple…