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There are two definitions of a metacyclic group. 1. A metacyclic group is a group G such that both its commutator subgroup G^' and the quotient group G/G^' are cyclic (Rose ...

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

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

The group theoretical term for what is known to physicists, by way of its connection with matrix traces, as the trace. The powerful group orthogonality theorem gives a number ...

A symmetry of a knot K is a homeomorphism of R^3 which maps K onto itself. More succinctly, a knot symmetry is a homeomorphism of the pair of spaces (R^3,K). Hoste et al. ...

The dihedral group D_n is the symmetry group of an n-sided regular polygon for n>1. The group order of D_n is 2n. Dihedral groups D_n are non-Abelian permutation groups for ...

The convolution of two complex-valued functions on a group G is defined as (a*b)(g)=sum_(k in G)a(k)b(k^(-1)g) where the support (set which is not zero) of each function is ...

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 study of groups. Gauss developed but did not publish parts of the mathematics of group theory, but Galois is generally considered to have been the first to develop the ...

O_h is the point group of symmetries of the octahedron having order 48 that includes inversion. It is also the symmetry group of the cube, cuboctahedron, and truncated ...