in amenable groups when applied to amenable groups. Since finite groups and abelian groups are amenable, every elementary amenable group is amenable -...

In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant...

for large classes of groups. For example, the zero-divisor conjecture is known for all torsion-free elementary amenable groups (a class including all...

in particular free groups) Elementary amenable groups (e.g. virtually abelian groups) Diffuse groups – in particular, groups that act freely isometrically...

{\displaystyle s} . Grigorchuk's group was also the first example of a group that is amenable but not elementary amenable, thus answering a problem posed...

exponential; an amenable linear group is virtually solvable, in particular elementary amenable; the von Neumann conjecture is true for linear groups. It is not...

finitely-presented groups: it is known that F is not elementary amenable. Higman (1974) introduced an infinite family of finitely presented simple groups, including...

mathematical subject of geometric group theory, an acylindrically hyperbolic group is a group admitting a non-elementary 'acylindrical' isometric action...

easily amenable geometric description, though this is the case for several important classes of groups, for instance Gromov-hyperbolic groups and arithmetic...

asymptotic cones of finitely generated groups (see e.g.); amenability of a finitely generated group; being virtually abelian (that is, having an abelian subgroup...

Those profinite groups with finite Prüfer rank are more amenable to analysis. Specifically in the case of finitely generated pro-p groups, having finite...

groups Herzog–Schönheim conjecture Subset sum problem Whitehead problem Word problem for groups Amenable group Capable group Commensurability (group theory)...

have appeared since. The isospectrality problem is in fact particularly amenable to study in the restricted setting of arithmetic manifolds. A fake projective...

locally compact amenable groups, following essentially the method of proof of Sz-Nagy. The result is known to fail for non-amenable groups such as SL(2,R)...

problems). Other group-theoretic topics like mapping class groups, property (T), solvability, amenability and lattices in Lie groups are sometimes regarded...

countable discrete group with property (T) is finitely generated. An amenable group which has property (T) is necessarily compact. Amenability and property...

contains a nonabelian free group (i.e., it has a subgroup isomorphic to the free group on two generators). A linear group is not amenable if and only if it contains...

light. Because they are point particles, their collisions are clean and amenable to precise measurements; however, because they are light, the collisions...

late 1800s. Early Portuguese and Italian immigrants found the climate amenable and planted thousands of acres of vineyards. Nearly 80 percent of Oakley's...

never to wear or break in pieces". The "primary" properties of matter were amenable to mathematical description, unlike "secondary" qualities such as color...

mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variables are the truth...

distinctions have also been made between hard systems—–technical in nature and amenable to methods such as systems engineering, operations research, and quantitative...

attach to a given variety X an object of more linear nature, i.e. an object amenable to the techniques of linear algebra, for example a vector space. This "linearization"...

problem, known as R = T theory, as opposed to the general G = T theory, was amenable to exact solutions in terms of a generalization of the Lambert W function...

Ax–Grothendieck theorem extends more broadly, to automata acting on amenable groups. Some partial converses to the Ax-Grothendieck Theorem: A generically...

amenable but not elementary amenable, thus providing an answer to another long-standing problem, posed by Mahlon Day in 1957. Also Grigorchuk's group...

addition, matrix multiplication). The algebraic objects amenable to such a description include groups, associative algebras and Lie algebras. The most prominent...

directly across Grand River Avenue. The company considered the location amenable to development because of its proximity to Grand River Avenue, a direct...

momentum and De Broglie wavelength), an asymptotically free theory is amenable to perturbation theory calculations using Feynman diagrams. Such situations...

with the charter, they can always migrate to a polis which appears more amenable to them. The most prominent differences between the various polises, at...