Related papers: A new family of sofic one-relator groups

A finitely generated solvable group with unbounded iterated identity is constructed.

The goal of this paper is to describe a theoretical construction of an infinite collection of non-classical Schottky groups. We first show that there are infinitely many non-classical noded Schottky groups on the boundary of Schottky space,…

We define a notion of relative soficity for countable groups with respect to a family of groups. A group is sofic if and only if it is relative sofic with respect to the family consisting only of the trivial group. If a group is relatively…

We prove that there exist finitely generated, stably finite algebras which are non linear sofic. This was left open by Arzhantseva and P\u{a}unescu in 2017.

We study two different types of (maximal) almost disjoint families: very mad families and (maximal) cofinitary groups. For the very mad families we prove the basic existence results. We prove that MA implies there exist many pairwise…

We present two families of numerical semigroups and show that for each family, the number of required components in an irreducible decomposition cannot be bounded by any given integer. This gives a negative answer to a question raised by…

We construct the first example of a finitely-presented, residually-finite group that contains an infinite sequence of non-isomorphic finitely-presented subgroups such that each of the inclusion maps induces an isomorphism of profinite…

We construct an infinite family of real cyclotomic fields with non-trivial class group. This result generalizes the result in [1] in the sense that our family includes theirs.

Let $G$ be a finite group and $\sigma_1(G)=\frac{1}{|G|}\sum_{H\leq G}\,|H|$. In this paper, we prove that if $\sigma_1(G)<2+\frac{11}{|G|}$\,, then $G$ is supersolvable. In particular, some new characterizations of the well-known groups…

We give the first example of a non-linear residually finite 1-related group: < a, t | a^{t^2}=a^2>.

Motivated by examples in infinite group theory, we classify the finite groups whose subgroups can never be decomposed as direct products.

Our main result is to show that every infinite, countable, residually finite group $G$ admits a Hausdorff group topology which is neither discrete nor precompact.

We perform the computations necessary to establish a multiplicity one statement for the irreducible representations of a finite spin group which in turn yields the classification of irreducible representations of finite spin groups. (The…

Let K be a set of infinite cardinals such that the cardinality of K is the first strong limit cardinal greater than uncountably many strong limit cardinals. We construct a family of pairwise non-embeddable groups which contains 2^k groups…

We construct a finitely presented (two-sided) totally orderable group with insoluble word problem.

We call a finite group irrational if none of its elements is conjugate to a distinct power of itself. We prove that those groups are solvable and describe certain classes of these groups, where the above property is only required for…

We determine the finite groups whose real irreducible representations have different degrees.

We introduce and systematically study linear sofic groups and linear sofic algebras. This generalizes amenable and LEF groups and algebras. We prove that a group is linear sofic if and only if its group algebra is linear sofic. We show that…

We provide polynomial lower bounds for residual finiteness of residually finite, finitely generated solvable groups that admit infinite order elements in the Fitting subgroup of strict distortion at least exponential. For this class of…

We show that any pseudofinite group with NIP theory and with a finite upper bound on the length of chains of centralisers is soluble-by-finite. In particular, any NIP rosy pseudofinite group is soluble-by-finite. This generalises, and…