Related papers: A note on torsion length

For all integers $p>q>0$ and $k >0$, and all non-elementary torsion-free hyperbolic groups $H$, we construct a hyperbolic group $G$ in which $H$ is a subgroup, such that the distortion function of $H$ in $G$ grows like $\exp^k(n^{p/q})$.…

An analogue of Burnside's Lemma for 2-transitive groups is shown to hold for a class of topological groups. If the group is compact the representation is finite and splits into an irreducible and the constant functions. If both the group…

We study a characteristic subgroup of finitely generated groups, consisting of elements with uniform upper bound for word-lengths. For a group $G$, we denote this subgroup by $G_{bound}$. We give sufficient criteria for triviality and…

We construct the first examples of infinite sharply 2-transitive groups which are finitely generated. Moreover, we construct such a group that has Kazhdan property (T), is simple, has exactly four conjugacy classes, and we show that this…

We provide involutory symmetric generating sets of finitely generated Coxeter groups, fulfilling a suitable finiteness condition, which in particular is fulfilled in the finite, affine and compact hyperbolic cases.

General coherence theorems are constructed that yield explicit presentations of categorical and algebraic objects. The categorical structures involved are finitary discrete Lawvere 2-theories, though they are approached within the language…

We initiate a study of infinite tensor products of projective unitary representations of a discrete group G. Special attention is given to regular representations twisted by 2-cocycles and to projective representations associated with…

We prove that each infinite 2-group with a unique 2-element subgroup is isomorphic either to the quasicyclic 2-group or to the infinite group of generalized quaternions.

This paper aims to give an account of theorem of Louder and Touikan which shows that many hierarchies consisting of slender JSJ-decompositions are finite. In particular JSJ-hierarchies of $2$-torsion-free hyperbolic groups are always…

In the context of Higman embeddings of recursive groups into finitely presented groups we suggest an algorithm which uses Higman operations to explicitly constructs the specific recursively enumerable sets of integer sequences arising…

The irreducible representations of all of the 80 diperiodic groups, being the symmetries of the systems translationally periodical in two directions, are calculated. To this end, each of these groups is factorized as the product of a…

We construct a finitely presented group with undecidable word problem and with Dehn function bounded by a quadratic function on an infinite set of positive integers.

A complete classification of finitely generated involutive commutative two-valued groups is obtained. Three series of such two-valued groups are constructed: principal, unipotent and special, and it is shown that any finitely generated…

This note collects several results on the capability of $p$-groups of class two and prime exponent. Among the new results, we settle the 4-generator case for this class.

Let $G$ be a finite 2-generated soluble group and suppose that $\langle a_1,b_1\rangle=\langle a_2,b_2\rangle=G$. If either $G^\prime$ is of odd order or $G^\prime$ is nilpotent, then there exists $b \in G$ with $\langle…

We prove that the generalised word problem of a finitely generated subgroup of a finitely generated virtually free group is context-free, that a hyperbolic group must be virtually free if it has a torsion-free quasiconvex subgroup of…

We prove that for a suitable class of representations of free group tensor products are generically irreducible. In particular we prove that there exist irreducible boundary realizations with infinite dimensional fiber.

We prove that the word problem for the infinite cyclic group is not EDT0L, and obtain as a corollary that a finitely generated group with EDT0L word problem must be torsion. In addition, we show that the property of having an EDT0L word…

We construct an uncountable family of 3-generated residually finite just-infinite groups with isomorphic profinite completions. We also show that word growth rate is not a profinite property.

We prove that both the hyperelliptic mapping class group and the extended hyperelliptic mapping class group are generated by two torsion elements. We also compute the index of the subgroup of the hyperelliptic mapping class group which is…