Finitely valued commutator sequences

Commutator Length of Finitely Generated Linear Groups

The commutator length “cl G ” of a group G is the least natural number c such that every element of the derived subgroup of G is a product of c commutators. We give an upper bound for cl G when G is a d-generator nilpotent-by-abelian-by-finite group. Then, we give an upper bound for the commutator length of a soluble-by-finite linear group over C that depends only on d and the degree of lineari...

Finitely Valued Indistinguishability Operators

Fuzzy equality relations or indistinguishability operators generalize the concepts of crisp equality and equivalence relations in fuzzy systems where inaccuracy and uncertainty is dealt with. They generate fuzzy granularity and are an essential tool in Computing with Words (CWW). Traditionally, the degree of similarity between two objects is a number between 0 and 1, but in many occasions this ...

Locally-finitely-valued Cohomology Groups

Finitely Generated Infinite Simple Groups of Infinite Commutator Width and Vanishing Stable Commutator Length

It is shown that there exists a finitely generated infinite simple group of infinite commutator width and infinite square width in which every conjugation-invariant norm is stably bounded, and in particular stable commutator length vanishes. Moreover, a recursive presentation of such a group with decidable word and conjugacy problems is constructed.

Finitely Generated Infinite Simple Groups of Infinite Commutator Width

It is shown that there exists a finitely generated infinite simple group of infinite commutator width, and that the commutator width of a finitely generated infinite boundedly simple group can be arbitrarily large. Besides, such groups can be constructed with decidable word and conjugacy problems.