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A group whose group operation is identified with multiplication. As with normal multiplication, the multiplication operation on group elements is either denoted by a raised ...

A finite group L is quasisimple if L=[L,L] and L/Z(L) is a simple group.

The cyclic group C_8 is one of the three Abelian groups of the five groups total of group order 8. Examples include the integers modulo 8 under addition (Z_8) and the residue ...

X is a p^'-group if p does not divide the group order of X.

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.

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

On a Riemannian manifold M, tangent vectors can be moved along a path by parallel transport, which preserves vector addition and scalar multiplication. So a closed loop at a ...

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.