Linked from

The 19 pages that link to Identity element, each with the reason it gives.

• GroupRelated: Every group has a neutral element for its operation.

• Fundamental groupRelated: The constant loop represents the identity in the fundamental group.

• Group homomorphismRelated: A group homomorphism sends the source identity to the target identity.

• SubgroupRelated: Every subgroup must contain the identity of the ambient group.

• Abstract algebraRelated: Identity elements give operations a neutral value and are required in groups.

• Cyclic groupRelated: The identity is the zeroth power of every generator and anchors its sequence of powers.

• Abelian groupRelated: Its existence is one of the group axioms inherited by Abelian groups.

• Binary operationRelated: Some binary operations have a neutral input that preserves the other input.

• Conjugacy classRelated: It forms a conjugacy class by itself in every group.

• MonoidRelated: Its presence distinguishes a monoid from a general semigroup.

• SemigroupRelated: A semigroup need not contain one, unlike a monoid.

• Associative propertyRelated: An associative operation with an identity has a particularly useful algebraic structure.

• Inverse elementRelated: The inverse is defined by combining to this element.

• Multiplicative orderRelated: The order is the first positive exponent at which the element’s powers reach this element.

• Commutative propertyRelated: An operation can have an identity element without being commutative.

• Fundamental theorem on homomorphismsRelated: The kernel consists of the elements mapped to the codomain's identity.