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The projective general unitary group PGU_n(q) is the group obtained from the general unitary group GU_n(q) on factoring the scalar matrices contained in that group.

The projective general linear group PGL_n(q) is the group obtained from the general linear group GL_n(q) on factoring by the scalar matrices contained in that group.

Rubik's group is the group corresponding to possible rotations of a Rubik's Cube. There are six possible rotations, each corresponding to a generator of the group, and the ...

Every finite group of order n can be represented as a permutation group on n letters, as first proved by Cayley in 1878 (Rotman 1995).

The projective symplectic group PSp_n(q) is the group obtained from the symplectic group Sp_n(q) on factoring by the scalar matrices contained in that group. PSp_(2m)(q) is ...

The general unitary group GU_n(q) is the subgroup of all elements of the general linear group GL(q^2) that fix a given nonsingular Hermitian form. This is equivalent, in the ...

The general orthogonal group GO_n(q,F) is the subgroup of all elements of the projective general linear group that fix the particular nonsingular quadratic form F. The ...

The study of a finite group G using the local subgroups of G. Local group theory plays a critical role in the classification theorem of finite groups.

The number of elements in a group G, denoted |G|. If the order of a group is a finite number, the group is said to be a finite group. The order of an element g of a finite ...

The icosahedral group I_h is the group of symmetries of the icosahedron and dodecahedron having order 120, equivalent to the group direct product A_5×Z_2 of the alternating ...