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The definition of amenability is simpler in the case of a discrete group, [4] i.e. a group equipped with the discrete topology. [5] Definition. A discrete group G is amenable if there is a finitely additive measure (also called a mean)—a function that assigns to each subset of G a number from 0 to 1—such that
It is conjectured that F is not amenable and hence a further counterexample to the long-standing but recently disproved von Neumann conjecture for finitely-presented groups: it is known that F is not elementary amenable. Higman (1974) introduced an infinite family of finitely presented simple groups, including Thompson's group V as a special case.
Amenable species is a term used within the context of USDA's meat and poultry inspection program to signify exotic species (livestock and fowl not covered by the statutes) that might be added to the laws and thus be eligible for mandatory federal inspection, which is taxpayer-funded. An exotic species is considered an amenable species if its ...
is necessarily finitely generated. In fact it is generated by every two non-commuting elements.; is simple. If and is any subgroup distinct from the subgroup would have elements.; The construction of Olshanskii shows in fact that there are continuum-many non-isomorphic Tarski Monster groups for each prime >.; Tarski monster groups are examples of non-amenable groups not containing any free ...
In mathematics, the von Neumann conjecture stated that a group G is non-amenable if and only if G contains a subgroup that is a free group on two generators. The conjecture was disproved in 1980. In 1929, during his work on the Banach–Tarski paradox , John von Neumann defined the concept of amenable groups and showed that no amenable group ...
A delusion [a] is a false fixed belief that is not amenable to change in light of conflicting evidence. [2] As a pathology, it is distinct from a belief based on false or incomplete information, confabulation, dogma, illusion, hallucination, or some other misleading effects of perception, as individuals with those beliefs are able to change or readjust their beliefs upon reviewing the evidence.
The name "sofic", from the Hebrew word סופי meaning "finite", was later applied by Weiss (2000), following Weiss's earlier use of the same word to indicate a generalization of finiteness in sofic subshifts. The class of sofic groups is closed under the operations of taking subgroups, extensions by amenable groups, and free products.
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