- - group on set with binary operator
- - group
- - binary operator
- - binary operator. Typically for additive groups
- - binary operator. Typically for multiplicative groups
- - group element
- - inverse of group element
- - identity element
- - identity element for additive groups
- - identity element for multiplicative groups
- - left identity
- - right identity
- - is a subgroup of
- - is a proper subgroup of
- - the size of group . Also called its order
- - the order of group element .
- - is isomorphic to .
- - a homomorphism
- - the kernel of homomorphism
- - the cyclic subgroup containing the generator .
- - the inner automorphism by .
- - conjugate subgroup using .
- - the set of all endomorphisms on .
- - the set of all automorphisms on .
- - the direct product of and .
- - the direct sum of and (assuming both are Abelian)
- - permutation
- - permutation applied times. (negative power means reversing the permutation)
- - orbit of a set on the element under the permutation .
- - Klein-4 group
- - General Linear Group on dimensions
- - Special Linear Group on dimensions.
- - Dihedral Group of order
- - Symmetric Group of order
- - Cyclic Group of order
- - Alternating group of order
- - generic normal group
- - commutator subgroup
- - Center of group .
- - torsion subgroup of abelian group
- - the left coset of containing
- - the right coset of containing .
- - the double coset.
- - is a normal subgroup of .
- - the index of .
- - the factor group of modulo
- - the orbit of under
- - the stabilizer of under .
- - subset of a -set where .