Related papers: Approximate (Abelian) groups

We find surface subgroups in certain one-relator groups with torsion and use this to deduce a profinite criterion for a word in the free group to be primitive.

A result of Pyber states that every finite group $G$ contains an abelian subgroup whose order is quasi-polynomially large in $\lvert G\rvert$. We prove a similar result for $K$-approximate subgroups of solvable groups under only modest…

In this short note we determine the set $\Phi^\infty(7)$ of Abelian groups that appear as torsion groups of infinitely many elliptic curves (up to $\overline \mathbb Q$-isomorphism) over number fields of degree 7.

We have reanalyzed a data set of 99 low redshift ($ z < 0.1 $) Abell clusters and determined their shapes. For this, three different measures are used. We use Monte-Carlo simulations to investigate the errors in the methods. The corrected…

By definition, a group is called narrow if it does not contain a copy of a non-abelian free group. We describe the structure of finite and narrow normal subgroups in Coxeter groups and their automorphism groups.

Partially ordered groups, also known as po-groups, are groups with a compatible partial order. Results from M.I. Zajceva and H.-H. Teh are combined in order to provide a full characterisation of linear order extensions of a given order on a…

We give a necessary and sufficient condition for a morphism between recollements of abelian categories to be an equivalence.

We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.

We completely characterize by finding necessary and sufficient conditions those co-Bassian and generalized co-Bassian Abelian groups having, respectively, the hereditary or the super property, thus giving a new insight in the full discovery…

The object of investigations are almost contact B-metric structures on 3-dimensional Lie groups considered as smooth manifolds. There are established the existence and some geometric characteristics of these manifolds in all basic classes.…

Difference sets are subsets of a group satisfying certain combinatorial property with respect to the group operation. They can be characterized using an equality in the group ring of the corresponding group. In this paper, we exploit the…

For a cardinal k, generalizing a recent result of Comfort and van Mill, we prove that every k-pseudocompact abelian group of weight >k has some proper dense k-pseudocompact subgroup and admits some strictly finer k-pseudocompact group…

A group is metabelian if its commutator subgroup is abelian. For finitely generated metabelian groups, classical commutative algebra, algebraic geometry and geometric group theory, especially the latter two subjects, can be brought to bear…

We introduce a notion of a group-partition for a finite Abelian group, which is a generalized notion of the standard partition. To obtain asymptoticdistributions of group-partition, we study the Dirichlet series for group-partitions by…

In this paper we discuss some of the key properties of sum-free subsets of abelian groups. Our discussion has been designed with a broader readership in mind, and is hence not overly technical. We consider answers to questions like: how…

Necessary and sufficient conditions for finite commutative semihypergroups to be built from abelian groups of the same order are established.

In this paper we study a relationship between elementary equivalence of endomorphism rings of Abelian p-groups and second order equivalence of the corresponding Abelian p-groups.

We will explore the nature of when certain finite groups have an equal covering, and when finite groups do not. Not to be confused with the concept of a cover group, a covering of a group is a collection of proper subgroups whose…

In this paper, we study precompact abelian groups G that contain no sequence {x_n} such that {0} \cup {\pm x_n : n \in N} is infinite and quasi-convex in G, and x_n --> 0. We characterize groups with this property in the following classes…

We give a characterization of the finite groups having nilpotent or abelian Hall $\pi$-subgroups which can easily be verified from the character table.