Properties of groups

group whose group operation is commutative

mathematical group that can be generated as the set of powers of a single element

group of symmetries of a regular polygon

mathematical group based upon a finite number of elements

group without normal subgroups other than the trivial group and itself

group that can be constructed from abelian groups using extensions; a group whose derived series terminates in the trivial subgroup

free object in the category of groups; a group admitting a presentation without any relations

group that is an algebraic variety

group that has an upper central series terminating with G

commutative group whose elements are unique integer combinations of basis elements

abelian group in which every element can, in some sense, be divided by positive integers

group in which each element has finite order

Wikimedia glossary list article

group such that every its subgroup is normal

Mathematical concept

group G that has some finite generating set S so that every element of G can be written as the product of finitely many elements of the finite set S and of inverses of such element

group with trivial abelianization

group where ab = ba does not always hold

Group realized geometrically by reflections across the sides of a triangle

group for which every surjective endomorphism is bijective

in mathematics, a solvable group that satisfies the maximal condition on subgroups

type of mathematical group

type of group

a topological group that is isomorphic to the inverse limit of an inverse system of solvable groups

way to measure distance between any two elements of group (in group theory)

a group that fits between a non-abelian simple group and its automorphism group

theorem that every subgroup of a free group is itself free

mathematical group that has no proper nontrivial characteristic subgroups

group G with abelian normal subgroup N and abelian quotient group G/N (equivalently: group with abelian commutator subgroup)