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A partially ordered set is defined as an ordered pair P=(X,<=). Here, X is called the ground set of P and <= is the partial order of P.

The kernel of a group homomorphism f:G-->G^' is the set of all elements of G which are mapped to the identity element of G^'. The kernel is a normal subgroup of G, and always ...

A group representation of a group G on a vector space V can be restricted to a subgroup H. For example, the symmetric group on three letters has a representation phi on R^2 ...

A group set is a set whose elements are acted on by a group. If the group G acts on the set S, then S is called a G-set. Let G be a group and let S be a G-set. Then for every ...

A general term which refers to an increase (or decrease in the case of the oxymoron "negative growth") in a given quantity.

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.

The problem of deciding if four colors are sufficient to color any map on a plane or sphere.

The gyroelongated pentagonal bicupola is the Johnson solid J_(46), which consists of two pentagonal cupolas, one twisted with respect to the other, adjoined to a decagonal ...

Johnson solid J_(48).

Johnson solid J_(25).