Related papers: Small cancellation groups are bi-exact

Given a finitely generated linear group $G$ over $\mathbb{Q}$, we construct a simple group $\Gamma$ that has the same finiteness properties as $G$ and admits $G$ as a quasi-retract. As an application, we construct a simple group of type…

We prove that if a Cartesian product of alternating groups is topologically finitely generated, then it is the profinite completion of a finitely generated residually finite group. The same holds for Cartesian producs of other simple groups…

Shephard groups are common extensions of Artin and Coxeter groups. They appear, for example, in algebraic study of manifolds. An infinite family of Shephard groups which are not Artin or Coxeter groups is considered. Using techniques form…

In this note, we classify all finite groups having exactly 6, 7 or 8 cyclic subgroups. This gives a partial answer to the open problem posed by Tarnauceanu (Amer. Math. Monthly, 122 (2015), 275-276). As a consequence of our results, we also…

We show that for $G$ a simple compact Lie group, the infinitesimal subgroup $G^{00}$ is bi-intepretable with a real closed valued field. We deduce that for $G$ an infinite definably compact group definable in an o-minimal expansion of a…

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

We determine all the ways in which a direct product of two finite groups can be expressed as the set-theoretical union of proper subgroups in a family of minimal cardinality.

We enumerate the 15768 perfect groups of order up to $2\cdot 10^6$, up to isomorphism, thus also completing the missing cases in the prior classification. The work supplements the by now well-understood computer classifications of solvable…

We provide two alternative ways to determine the number of (bi-)twisted conjugacy classes in a finite group: one by counting certain irreducible characters and one by counting certain twisted conjugacy classes of other endomorphisms. In…

We provide a proof that the classes of finitely generated Kleinian groups and of three-manifold groups are quasi-isometrically rigid.

In this article we prove results about finite soluble groups that act with fixity 2 or 3.

Groups of finite type (also called finitely constrained groups), introduced by Grigorchuk, are known to be the closure of regular branch groups. This article explores many of their properties. Firstly, we prove that being finitely…

Given a discrete (resp. profinite) group $G$, we define $NCC(G)$ to be the smallest number of cyclic (resp. procyclic) subgroups of $G$ whose conjugates cover $G$. In this paper we determine all residually finite discrete groups with finite…

We give a construction of a family of locally finite residually finite groups with just-infinite C*-algebra. This answers a question from [2]. Additionally, we show that residually finite groups of finite exponent are never just-infinite.

We provide an analogue of Strebel's classification of geodesic triangles in classical $C'(\frac16)$ groups for groups given by Wise's cubical presentations satisfying sufficiently strong metric cubical small cancellation conditions. Using…

We give examples of finite quantum permutation groups which arise from the twisting construction or as bicrossed products associated to exact factorizations in finite groups. We also give examples of finite quantum groups which are not…

We construct a finitely generated 2-dimensional group that acts properly on a locally finite CAT(0) cube complex but does not act properly on a finite dimensional CAT(0) cube complex.

We characterize the group property of being with infinite conjugacy classes (or icc, i.e. \not= 1 and of which all conjugacy classes except 1 are infinite) for finite extensions of group.

We study systematically groups whose marked finite quotients form a recursive set. We give several definitions, and prove basic properties of this class of groups, and in particular emphasize the link between the growth of the depth…

We produce new short laws in two variables valid in finite groups of Lie type. Our result improves upon results of Kozma and the second named author, and is sharp up to logarithmic factors, for all families except possibly the Suzuki…