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An abstract group is a group characterized only by its abstract properties and not by the particular representations chosen for elements. For example, there are two distinct ...

A group having an infinite number of elements. Some infinite groups, such as the integers or rationals, are not continuous groups.

The study of a finite group G using the local subgroups of G. Local group theory plays a critical role in the classification theorem of finite groups.

A group of linear fractional transformations which transform the arguments of Kummer solutions to the hypergeometric differential equation into each other. Define A(z) = 1-z ...

The baby monster group, also known as Fischer's baby monster group, is the second-largest sporadic group. It is denoted B and has group order |B| = ...

A finitely generated discontinuous group of linear fractional transformations z->(az+b)/(cz+d) acting on a domain in the complex plane. The Apollonian gasket corresponds to a ...

The convolution of two complex-valued functions on a group G is defined as (a*b)(g)=sum_(k in G)a(k)b(k^(-1)g) where the support (set which is not zero) of each function is ...

Given a knot diagram, it is possible to construct a collection of variables and equations, and given such a collection, a group naturally arises that is known as the group of ...

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

A group action of a topological group G on a topological space X is said to be a proper group action if the mapping G×X->X×X(g,x)|->(gx,x) is a proper map, i.e., inverses of ...