Linked from

The 51 pages that link to Group, each with the reason it gives.

• Vector spaceNarrower topic: Vector addition makes each vector space an abelian group.

• Group actionNarrower topic: Its multiplication determines how successive transformations must combine.

• Lie groupNarrower topic: Its algebraic axioms remain part of a Lie group’s definition.

• Representation theoryNarrower topic: Group representations assign invertible linear maps to group elements while preserving their multiplication.

• Field (mathematics)Narrower topic: Each field operation forms a group: addition on all elements and multiplication on nonzero elements.

• Group homomorphismNarrower topic: Homomorphisms compare groups by preserving their operations.

• Finite groupNarrower topic: Finite groups are groups whose underlying sets happen to be finite.

• Quotient groupNarrower topic: A quotient group inherits its operation’s group laws from the original group.

• SubgroupNarrower topic: A subgroup inherits its operation and identity from this larger structure.

• Évariste GaloisNarrower topic: Group structure makes the symmetries of polynomial roots mathematically tractable.

• Permutation groupNarrower topic: Permutation groups satisfy the group axioms under composition.

• Cyclic groupNarrower topic: Cyclicity is a property of groups, defined through repeated application of their operation.

• Group representationNarrower topic: A representation starts with a group and translates its operation into composition of linear maps.

• Algebraic topologyNarrower topic: Fundamental groups encode how loops in a space combine under concatenation.

• Galois theoryNarrower topic: Galois groups bring group structure to the symmetries of algebraic extensions.

• Abelian groupNarrower topic: An Abelian group is precisely a group that also satisfies commutativity.

• CosetNarrower topic: Cosets are formed inside groups using their operation.

• Orbit-stabilizer theoremNarrower topic: The theorem measures orbits using the order of this algebraic structure.

• Cayley graphNarrower topic: Its elements supply the vertices, while its operation defines each edge.

• Conjugacy classNarrower topic: Conjugacy classes are defined using the group's operation and inverses.

• Lagrange's theoremNarrower topic: Lagrange’s theorem is a statement about the sizes of groups and their subgroups.

• Symmetry groupNarrower topic: A symmetry group is a group whose elements are structure-preserving transformations.

• Free groupNarrower topic: Free groups are groups whose elements are built from generators while obeying these axioms.

• Division ringNarrower topic: The nonzero elements of a division ring form a group under multiplication.

• Finite simple groupNarrower topic: Finite simple groups are groups whose normal-subgroup structure admits no proper nontrivial part.

• Cayley's theoremNarrower topic: The theorem applies to every structure satisfying these group axioms.

• Finite cyclic groupNarrower topic: Finite cyclic groups satisfy the group axioms under their defining operation.

• Multiplicative orderNarrower topic: Multiplicative order is defined for elements of any group, not only numbers.

• Rotation groupNarrower topic: A rotation group is a group whose elements are geometric rotations.

• CentralizerNarrower topic: A centralizer is defined inside a group and inherits its operation.

• Ring theoryNarrower topic: Ring addition is required to form an abelian group.

• Zassenhaus lemmaNarrower topic: The lemma applies to subgroup configurations inside a single group.

• Herzog–Schönheim conjectureNarrower topic: The conjecture concerns partitions of groups by subgroup cosets.