group
algebraic set with an invertible, associative internal operation admitting a neutral element
matrix group
group consisting of invertible matrices over a field
quotient group
group obtained by aggregating similar elements of a larger group
perfect group
group with trivial abelianization
additive group
group of which the group operation is to be thought of as addition
Covering group
concept in topological group theory
generalized symmetric group
wreath product of cyclic group m and symetrical group n
non-abelian group
group where ab = ba does not always hold
triangle group
Group realized geometrically by reflections across the sides of a triangle
modular group
orientation-preserving mapping class group of the torus
characteristically simple group
mathematical group that has no proper nontrivial characteristic subgroups
Saint Joseph and the Christ Child
painting by Giovanni Battista Tiepolo
Raphael Rooms
suite of reception rooms in the Palace of the Vatican painted by Raphael and his workshop between 1509 and 1524
symmetry group
group of transformations under which the object is invariant
multiplicative group
several notions
covering groups of the alternating and symmetric groups
type of a group
cyclically ordered group
group with a cyclic order respected by the group operation
generalized dihedral group
Family of groups in mathematics
subgroup
subset of a mathematical group that forms a group itself
permutation group
group whose operation is composition of permutations
T-group
group in which every subnormal subgroup is normal
point group
group of geometric symmetries (isometries) that keep at least one point fixed
topological group
group that is a topological space with continuous group action
discrete group
discrete subgroup of a topological group G is a subgroup H such that there is an open cover of H in which every open subset contains exactly one element of H; in other words, the subspace topology of H in G is the discrete topology
ordered group
group with a compatible partial order
direct product of groups
operation in which it takes certain group and creates another
CA-group
group in which the centralizer of a non-identity element is abelian
Cremona group
the group of birational automorphisms of the n-dimensional projective space over a field k
thin group
group whose girths of the Cayley graphs induced by any finite generating set are bounded above
finitely generated group
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
automorphism group
mathematical group formed from the automorphisms of an object
hyperbolic group
Mathematical concept
group extension
group for which a given group is a normal subgroup
point groups in three dimensions
groups of point isometries in 3 dimensions
tame group
type of mathematical group
infinite group
group, of which the underlying set contains an infinite number of elements
torsion group
group in which each element has finite order
wreath product
operation on two groups in group theory
almost simple group
a group that fits between a non-abelian simple group and its automorphism group
locally finite group
type of group
Z-group
group whose Sylow subgroups are cyclic
outer automorphism group
Mathematical group