Linked from

The 9 pages that link to Inverse element, each with the reason it gives.

• GroupRelated: Each group element must have a partner that reverses its effect.

• Fundamental groupRelated: Reversing a loop gives the class that cancels it under concatenation.

• Group homomorphismRelated: Preservation of products forces homomorphisms to preserve inverses.

• SubgroupRelated: Subgroup membership requires inverses to remain in the subset.

• Identity elementRelated: The identity is the target result in the definition of an inverse.

• Abelian groupRelated: Every element of an Abelian group must have an inverse.

• Binary operationRelated: In operations with an identity, inverses can undo the effect of individual elements.

• Associative propertyRelated: Inverses become central when an associative operation also has an identity.

• Commutative propertyRelated: Inverses are defined relative to an operation; their existence does not itself imply commutativity.