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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 ...

The dihedral group D_4 is one of the two non-Abelian groups of the five groups total of group order 8. It is sometimes called the octic group. An example of D_4 is the ...

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 ...

The projective special unitary group PSU_n(q) is the group obtained from the special unitary group SU_n(q) on factoring by the scalar matrices contained in that group. ...

Given two groups G and H, there are several ways to form a new group. The simplest is the direct product, denoted G×H. As a set, the group direct product is the Cartesian ...

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 finite group C_2×C_6 is the finite group of order 12 that is the group direct product of the cyclic group C2 and cyclic group C6. It is one of the two Abelian groups of ...

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, ...

A finitely presented group is a group with a finite number of generators and relations. A mathematical joke involving finitely presented groups is given by Renteln and Dundes ...

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 ...