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A ring without zero divisors in which an integer norm and an associated division algorithm (i.e., a Euclidean algorithm) can be defined. For signed integers, the usual norm ...

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 ...

An arrangement of points with no three collinear, or of lines with no three concurrent.

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 ...

Regardless of where one white and one black square are deleted from an ordinary 8×8 chessboard, the reduced board can always be covered exactly with 31 dominoes (of dimension ...

Two groups G and H are said to be isoclinic if there are isomorphisms G/Z(G)->H/Z(H) and G^'->H^', where Z(G) is the group center of the group, which identify the two ...

Any linear system of point-groups on a curve with only ordinary singularities may be cut by adjoint curves.

Any irreducible curve may be carried by a factorable Cremona transformation into one with none but ordinary singular points.

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.

The projective general orthogonal group PGO_n(q) is the group obtained from the general orthogonal group GO_n(q) on factoring the scalar matrices contained in that group.