Group theory

analogue of the definition of a group inside an arbitrary category

Symmetry principle

properties underlying modern physics

cohomology theory associated to a group 𝐺 and a 𝐺‐module

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

homomorphism G → PGL(V) from a group G to a projective linear group PGL(V) over a vector space V

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regular polygonal symmetries

highly-symmetric node-link graph with 100 vertices and 22 edges per vertex

basic construction of combinatorial group theory

metric space in which every two points are connected by a unique geodesic arc

thumb|The torus can be made an abelian group isomorphic to the product of the [[circle group. This abelian group is a Klein four-group-module, where the group acts by reflection in each of the coordinate directions (here depicted by red and blue arrows intersecting at the identity element).]]

isometry of the Eluclidean plane

theorem about admissible crystal symmetries

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mathematical structure

concept in module theory

algebraic structure

minimal cardinality of a generating set of the group

generalised concept of incidence structure of polygons

function defined on the set of conjugacy classes of a group

structure on Lie groups

group of group homomorphisms from a group into the multiplication group of nonzero elements of a field

term

largest normal subgroup that is contained in a given subgroup

probabilistic algorithm for computing discrete logarithms

efficient algorithm to count points on elliptic curves

highly-symmetric node-link graph with 100 vertices and 36 edges per vertex

research proposal by A. Grothendieck

system of classifying symmetry groups, describing the angles between with fundamental reflections of a Coxeter group in a bracketed notation, with modifiers to indicate certain subgroups

check digit algorithm presented by H. Michael Damm

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

written product of elements of a mathematical group and their inverses

closure of the set of conjugate elements under the group operation

Concept in math

the group of birational automorphisms of the n-dimensional projective space over a field k

the theorem that extending ideals gives a mapping on the class group of an algebraic number field to the class group of its Hilbert class field, which sends all ideal classes to the class of a principal ideal

set containing exactly one element from each member of a family of sets

semidirect product of a group with its automorphism group

given a finitely generated group, the algorithmic problem of deciding whether two words in the generators represent the same element

concept in Galois theory

Mathematical group