0,k](n) is equal to the number of elements in the colored

permutation group [G.

r](Q) is a normal subgroup, then the equivalence relation induced by the orbits ofthe right-regular

permutation group R([?

The orbital profile of a

permutation group G acting on a set E is the function [[theta].

1 (Cayley Theorem) Every group is isomorphic to a

permutation group.

Let n a positive integer and G a

permutation group G [subset] [G.

This is surprising since, on the full

permutation group, separation requires 2 [log.

While this line of research on growth started with the study of matrix groups, it has now given strong results on

permutation groups as well.

Second parameter: number of

permutation groups (k), or hash function groups.

Writing in a style that attempts to preserve the informal flavor of the classroom, Isaacs (mathematics, University of Wisconsin) covers subnormality, split extensions, commutators, Frobenius actions, and

permutation groups.

He reviews linear algebras, then describes the group and its subsets, including homomorphism of two groups and the proper symmetric group of a regular polyhedron, the theory of linear representations of groups, the three-dimensional rotation group,

permutation groups, Lie groups and Lie algebras, unitary groups, real orthogonal groups and symplectic groups.

He then considers the work of Lagrange, Galois and Kronecker in concert, the process of computing Galois groups, solvable

permutation groups, and the lemniscate, including the lemniscatic function, complex multiplication and Abel's theorem.

Remmel, Descents, major indices, and inversions in

permutation groups, Discrete Mathematics, Vol.