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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 cyclic group C_(11) is unique group of group order 11. An example is the integers modulo 11 under addition (Z_(11)). No modulo multiplication group is isomorphic to ...

The cyclic group C_9 is one of the two Abelian groups of group order 9 (the other order-9 Abelian group being C_3×C_3; there are no non-Abelian groups of order 9). An example ...

A subgroup H of an original group G has elements h_i. Let x be a fixed element of the original group G which is not a member of H. Then the transformation xh_ix^(-1), (i=1, ...

The study of groups. Gauss developed but did not publish parts of the mathematics of group theory, but Galois is generally considered to have been the first to develop the ...

Frucht's theorem states that every finite group is the automorphism group of a finite undirected graph. This was conjectured by König (1936) and proved by Frucht (1939). In ...

An extension of a group H by a group N is a group G with a normal subgroup M such that M=N and G/M=H. This information can be encoded into a short exact sequence of groups ...

Each of the sets forming a direct product is said to be a direct factor. A group G is said to be a direct factor of the group G^' if G^' is isomorphic to the group direct ...

The value at a stationary point.

Let f(z) be an analytic function in an angular domain W:|argz|<alphapi/2. Suppose there is a constant M such that for each epsilon>0, each finite boundary point has a ...