In group theory, more precisely in geometric group theory, a hyperbolic group, also known as a word hyperbolic group or Gromov hyperbolic group, is a finitely...

In mathematics, relatively hyperbolic groups form an important class of groups of interest for geometric group theory. The main purpose in their study...

or the hyperbolic plane. Fuchsian groups are, by definition, discrete subgroups of the isometry group of the hyperbolic plane. A Fuchsian group that preserves...

geometric group theory, an acylindrically hyperbolic group is a group admitting a non-elementary 'acylindrical' isometric action on some geodesic hyperbolic metric...

"Hyperbolic groups" that introduced the notion of a hyperbolic group (also known as word-hyperbolic or Gromov-hyperbolic or negatively curved group),...

classical hyperbolic geometry and of trees. Hyperbolicity is a large-scale property, and is very useful to the study of certain infinite groups called Gromov-hyperbolic...

subdivided, e.g. into hyperbolic and other Coxeter groups. However, there are multiple non-equivalent definitions for hyperbolic Coxeter groups. We use the following...

a group-theoretical background. In a similar vein, geometric group theory employs geometric concepts, for example in the study of hyperbolic groups. Further...

In mathematics, a Kleinian group is a discrete subgroup of the group of orientation-preserving isometries of hyperbolic 3-space H3. The latter, identifiable...

in geometric group theory and have led to generalizations such as limit groups over hyperbolic and certain relatively hyperbolic groups. Basic examples...

In mathematics, hyperbolic space of dimension n is the unique simply connected, n-dimensional Riemannian manifold of constant sectional curvature equal...

the action of Kleinian group by Möbius transformations on the ideal boundary S 2 {\displaystyle \mathbb {S} ^{2}} of the hyperbolic 3-space H 3 {\displaystyle...

In mathematics, hyperbolic geometry (also called Lobachevskian geometry or Bolyai–Lobachevskian geometry) is a non-Euclidean geometry. The parallel postulate...

of the hyperbolic plane, or conformal transformations of the unit disc, or conformal transformations of the upper half plane, so a Fuchsian group can be...

In mathematics and group theory, the term multiplicative group refers to one of the following concepts: the group under multiplication of the invertible...

boundary of a δ-hyperbolic space (especially a hyperbolic group) is an abstract concept generalizing the boundary sphere of hyperbolic space. Conceptually...

sphere, or a hyperbolic triangle. Each triangle group is the symmetry group of a tiling of the Euclidean plane, the sphere, or the hyperbolic plane by congruent...

center of mass – associated with hyperbolic rotations between each spatial dimension and time The Poincaré group is the group of Minkowski spacetime isometries...

Cartan matrices correspond to hyperbolic Coxeter group. But in general, most negative determinant matrices are neither hyperbolic nor Lorentzian. Finite branches...

finite groups, or just the sporadic groups. A simple group is a group G that does not have any normal subgroups except for the trivial group and G itself...

established a negative solution to an analogue of the Burnside problem for hyperbolic groups, provided the exponent is sufficiently large. By contrast, when the...

each of the elements of the modular group, a regular tessellation of the hyperbolic plane by congruent hyperbolic triangles known as the V6.6.∞ Infinite-order...

finite index n. Every abelian subgroup of a Gromov hyperbolic group is virtually cyclic. A profinite group is called procyclic if it can be topologically...

uniform polytopes in hyperbolic 9-dimensional space. T ¯ 9 {\displaystyle {\bar {T}}_{9}} , also (E10) is a paracompact hyperbolic group, so either facets...

known as group theory, the monster group M (also known as the Fischer–Griess monster, or the friendly giant) is the largest sporadic simple group; it has...

euclidean, hyperbolic or projective geometry) using group theory, Felix Klein initiated the Erlangen programme. Sophus Lie, in 1884, started using groups (now...

wider class of groups, for example Gromov-hyperbolic groups. Since for any n ≥ 2, the free group on 2 generators F2 contains the free group on n generators...

In group theory, the Tits group 2F4(2)′, named for Jacques Tits (French: [tits]), is a finite simple group of order    17,971,200 = 211 · 33 · 52 · 13...

mathematics, an abelian group, also called a commutative group, is a group in which the result of applying the group operation to two group elements does not...

In group theory, a dicyclic group (notation Dicn or Q4n, ⟨n,2,2⟩) is a particular kind of non-abelian group of order 4n (n > 1). It is an extension of...