Finite subset spaces of graphs and punctured surfaces.
Finite Sylow subgroups in simple locally finite groups of Lie type.
Finite tangled groups.
Finite-finitary, polycyclic-finitary and Chernikov-finitary automorphism groups
If X is a property or a class of groups, an automorphism ϕ of a group G is X-finitary if there is a normal subgroup N of G centralized by ϕ such that G/N is an X-group. Groups of such automorphisms for G a module over some ring have been very extensively studied over many years. However, for groups in general almost nothing seems to have been done. In 2009 V. V. Belyaev and D. A. Shved considered the general case for X the class of finite groups. Here we look further at the finite case but our main...
Finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups
We study infinite finitely generated groups having a finite set of conjugacy classes meeting all cyclic subgroups. The results concern growth and the ascending chain condition for such groups.
Finitely Generated pro-2 Groups with a free subgroup of Index 2.
Finitely generated soluble groups with an Engel condition on infinite subsets
Finitely generated soluble groups with an Engel condition on infinite subsets
Finitely Presented Subgroups of Three-Manifold Groups.
Finiteness properties of soluble arithmetic groups over global function fields.
Finite-valued subgroups of lattice-ordered groups
Finitude géométrique en géométrie de Hilbert
On étudie la notion de finitude géométrique pour certaines géométries de Hilbert définies par un ouvert strictement convexe à bord de classe .La définition dans le cadre des espaces Gromov-hyperboliques fait intervenir l’action du groupe discret considéré sur le bord de l’espace. On montre, en construisant explicitement un contre-exemple, que cette définition doit être renforcée pour obtenir des définitions équivalentes en termes de la géométrie de l’orbifold quotient, similaires à celles obtenues...
First Order Classes of Groups Having no Groups With a Given Property
First-order definability and algebraicity of the sets of annihilating and generating collections of elements for some relatively free solvable groups.
Fixed points for positive permutation braids
Making use of the Nielsen fixed point theory, we study a conjugacy invariant of braids, which we call the level index function. We present a simple algorithm for computing it for positive permutation cyclic braids.
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
Fixed points of endomorphisms of certain free products
The fixed point submonoid of an endomorphism of a free product of a free monoid and cyclic groups is proved to be rational using automata-theoretic techniques. Maslakova’s result on the computability of the fixed point subgroup of a free group automorphism is generalized to endomorphisms of free products of a free monoid and a free group which are automorphisms of the maximal subgroup.
Flats in 3-manifolds
Flats in Spaces with Convex Geodesic Bicombings
In spaces of nonpositive curvature the existence of isometrically embedded flat (hyper)planes is often granted by apparently weaker conditions on large scales.We show that some such results remain valid for metric spaces with non-unique geodesic segments under suitable convexity assumptions on the distance function along distinguished geodesics. The discussion includes, among other things, the Flat Torus Theorem and Gromov’s hyperbolicity criterion referring to embedded planes. This generalizes...
Flows and joins of metric spaces.