Definition:Commutator of Group Elements/Definition 1

Definition

Let $\struct {G, \circ}$ be a group.

Let $g, h \in G$.

The commutator of $g$ and $h$ is the element of $G$ defined and denoted:

$\sqbrk {g, h} := g^{-1} \circ h^{-1} \circ g \circ h$

Also see

• Equivalence of Definitions of Commutator of Group Elements

• Results about commutators of group elements can be found here.

Sources

• 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): Chapter $8$: Homomorphisms, Normal Subgroups and Quotient Groups: Exercise $15$
• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): commutator: 1.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): commutator
• 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): commutator