commutator length
"Commutator length" is a concept used in group theory to measure the complexity of elements in a group in terms of commutators.
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Definition
C2Group Theory
(technical, academic)The minimum number of commutators required to express an element as a product of commutators.
Example
- The commutator length of the element in the group was determined to be three.
- Understanding commutator length helps in analyzing the structure of a group.
C2Topological Spaces
(technical, academic)The smallest number of commutators needed to represent a loop in the fundamental group of a space.
Example
- In the study of topological spaces, the commutator length of a loop can provide insights into the space's fundamental group.
- Researchers calculated the commutator length of various loops to understand the topological properties of the space.