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A particular type of automorphism group which exists only for groups. For a group G, the outer automorphism group is the quotient group Aut(G)/Inn(G), which is the ...

A conic section on which the midpoints of the sides of any complete quadrangle lie. The three diagonal points P, Q, and R also lie on this conic.

A set of points which do not lie on any of a certain class of hyperplanes.

A point which does not lie on at least one ordinary line.

A representation of a group G is a group action of G on a vector space V by invertible linear maps. For example, the group of two elements Z_2={0,1} has a representation phi ...

The group of rotations and translations.

Some elements of a group G acting on a space X may fix a point x. These group elements form a subgroup called the isotropy group, defined by G_x={g in G:gx=x}. For example, ...

The projective special orthogonal group PSO_n(q) is the group obtained from the special orthogonal group SO_n(q) on factoring by the scalar matrices contained in that group. ...

The double covering group of the (linear) symplectic group.

In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), ...