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If G is a perfect group, then the group center of the quotient group G/Z(G), where Z(G) is the group center of G, is the trivial group.

A group action G×X->X is effective if there are no trivial actions. In particular, this means that there is no element of the group (besides the identity element) which does ...

Any linear system of point-groups on a curve with only ordinary singularities may be cut by adjoint curves.

A complete set of mutually conjugate group elements. Each element in a group belongs to exactly one class, and the identity element (I=1) is always in its own class. The ...

An orbifold is the object obtained by identifying any two points of a map which are equivalent under some symmetry of the map's group.

If a map f:G->G^' from a group G to a group G^' satisfies f(ab)=f(b)f(a) for all a,b in G, then f is said to be an antihomomorphism.

A group L is a component of H if L is a quasisimple group which is a subnormal subgroup of H.

A prime factorization algorithm.

A finite group G has a finite number of conjugacy classes and a finite number of distinct irreducible representations. The group character of a group representation is ...

A p-elementary subgroup of a finite group G is a subgroup H which is the group direct product H=C_n×P, where P is a p-group, C_n is a cyclic group, and p does not divide n.