Search Results for ""

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 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 ...

A free Abelian group is a group G with a subset which generates the group G with the only relation being ab=ba. That is, it has no group torsion. All such groups are a direct ...

In celestial mechanics, the fixed path a planet traces as it moves around the sun is called an orbit. When a group G acts on a set X (this process is called a group action), ...

For a group G and a normal subgroup N of G, the quotient group of N in G, written G/N and read "G modulo N", is the set of cosets of N in G. Quotient groups are also called ...

An alternating group is a group of even permutations on a set of length n, denoted A_n or Alt(n) (Scott 1987, p. 267). Alternating groups are therefore permutation groups. ...

Let K be a number field and let O be an order in K. Then the set of equivalence classes of invertible fractional ideals of O forms a multiplicative Abelian group called the ...

Given a ring R with identity, the special linear group SL_n(R) is the group of n×n matrices with elements in R and determinant 1. The special linear group SL_n(q), where q is ...

A solvable group is a group having a normal series such that each normal factor is Abelian. The special case of a solvable finite group is a group whose composition indices ...

Given two normal subgroups G_1 and G_2 of a group, and two normal subgroups H_1 and H_2 of G_1 and G_2 respectively, H_1(G_1 intersection H_2) is normal in H_1(G_1 ...