Related papers: Proper decompositions of finitely presented groups

We study the problem of deciding whether or not the image of an irreducible representation of the braid group $\B_3$ of degree $\leq 5$ has finite image if we are only given the eigenvalues of a generator. We provide a partial algorithm…

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.

We introduce a novel interpretable tree based algorithm for prediction in a regression setting. Our motivation is to estimate the unknown regression function from a functional decomposition perspective in which the functional components…

We construct tree-decompositions of graphs that distinguish all their k-blocks and tangles of order k, for any fixed integer k. We describe a family of algorithms to construct such decompositions, seeking to maximize their diversity subject…

We define a cell complex with an action of the even spin mapping class group, and use it to obtain a finite presentation. We also obtain a finite presentation with Dehn twist generators.

In this paper we survey some recent results on actions of finite groups on topological manifolds. Given an action of a finite group $G$ on a manifold $X$, these results provide information on the restriction of the action to a subgroup of…

We prove that certain Fuchsian triangle groups are profinitely rigid in the absolute sense, i.e. each is distinguished from all other finitely generated, residually finite groups by its set of finite quotients. We also develop a method…

We formulate the Root Extraction problem in finite Abelian $p$-groups and then extend it to generic finite Abelian groups. We provide algorithms to solve them. We also give the bounds on the number of group operations required for these…

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

The residual finiteness growth of a group quantifies how well approximated the group is by its finite quotients. In this paper, we construct groups with arbitrarily large residual finiteness growth. We also demonstrate a new relationship…

We introduce a batched lazy algorithm for supervised classification using decision trees. It avoids unnecessary visits to irrelevant nodes when it is used to make predictions with either eagerly or lazily trained decision trees. A set of…

We study fundamental groups of non compact Riemannian manifolds. We find conditions which ensure that the fundamental group is trivial, finite or finitely generated.

Broadly speaking, a finiteness property of groups is any generalisation of the property of having finite order. A large part of infinite group theory is concerned with finiteness properties and the relationships between them. Profinite…

Classification of datasets into two or more distinct classes is an important machine learning task. Many methods are able to classify binary classification tasks with a very high accuracy on test data, but cannot provide any easily…

We present a theoretical algorithm which, given any finite presentation of a group as input, will terminate with answer yes if and only if the group is large. We then implement a practical version of this algorithm using Magma and apply it…

We define a class of finite groups based on the properties of the closed twins of their power graphs and study the structure of those groups. As a byproduct, we obtain results about finite groups admitting a partition by cyclic subgroups.

The finite orbits of the braid group action on Stokes matrices are studied and are shown to be the orbits on ordered sets of reflections, generating finite groups. All invariants of a reflection arrangement are determined. Determination of…

We study non-nesting actions of groups on real trees. We prove some fixed point theorems for such actions under the assumption that groups are Polish and have comeagre conjugacy classes.

We give an example of a finitely presented simple group containing a finitely generated subgroup which is not finitely presented.

Fixed-parameter tractable (FPT) algorithms have been successfully applied to many intractable problems -- with a focus on decision and optimization problems. Their aim is to confine the exponential explosion to some parameter, while the…