Search Results for ""

When the group order h of a finite group is a prime number, there is only one possible group of group order h. Furthermore, the group is cyclic.

C_6 is one of the two groups of group order 6 which, unlike D_3, is Abelian. It is also a cyclic. It is isomorphic to C_2×C_3. Examples include the point groups C_6 and S_6, ...

The finite group C_2×C_2 is one of the two distinct groups of group order 4. The name of this group derives from the fact that it is a group direct product of two C_2 ...

The quaternion group is one of the two non-Abelian groups of the five total finite groups of order 8. It is formed by the quaternions +/-1, +/-i, +/-j, and +/-k , denoted Q_8 ...

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

A cycle graph of a group is a graph which shows cycles of a group as well as the connectivity between the cycles. Such graphs are constructed by drawing labeled nodes, one ...

The set of all nonsingular affine transformations of a translation in space constitutes a group known as the affine group. The affine group contains the full linear group and ...

A continuous group G which has the topology of a T2-space is a topological group. The simplest example is the group of real numbers under addition. The homeomorphism group of ...

The group of rotations and translations.

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 ...