On single commutators in II$_{1}$–factors

On Commutators in Groups

Commutators originated over 100 years ago as a by-product of computing group characters of nonabelian groups. They are now an established and immensely useful tool in all of group theory. Commutators became objects of interest in their own right soon after their introduction. In particular, the phenomenon that the set of commutators does not necessarily form a subgroup has been well documented ...

Commutators on ` ∞

The operators on `∞ which are commutators are those not of the form λI + S with λ 6= 0 and S strictly singular.

ON COMMUTATORS IN p-GROUPS

For a given prime p, what is the smallest integer n such that there exists a group of order p in which the set of commutators does not form a subgroup? In this paper we show that n = 6 for any odd prime and n = 7 for p = 2.

On Subgroup Commutators

On Commutators of Isometries and Hyponormal Operators

A sufficient condition is obtained for two isometries to be unitarily equivalent. Also, a new class of M-hyponormal operator is constructed