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If two groups are residual to a third, every group residual to one is residual to the other. The Gambier extension of this theorem states that if two groups are ...

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).

An n-gonal pyramid adjoined to the top of an n-gonal antiprism. In the 3-gonal gyroelongated pyramid, the pyramid and lateral antiprism are coplanar. However, the 4-gonal and ...

Johnson solid J_(45).