In particular, we will use q-ary lattices and their

cosets which are defined as follows:

So the double

cosets for [[GAMMA].sub.0](p) have representatives of the form

A suggestive formulation is to suppose that A [??] R and to ask how often a

coset [gamma] + cZ, where c [member of] R, of a discrete subgroup cZ of R meets A.

There exists a subgroup H of finite index in G, which does not intersect F, and such that the right

cosets Hu, u [member of] F, are pairwise disjoint.

Mushtaq, "A condition for the existence of a fragment of a

coset diagram," The Quarterly Journal of Mathematics, vol.

More precisely, our result reduces to the Bruhat decomposition of the Lie groups [D.sub.n] relative to the parabolic subsystem [A.sub.n-1], so reflections are actually equivalence classes corresponding to n + 1

cosets of the parabolic Weyl group.

* To set up the equation, continue sampling for the

cosets obtained from the columns of the matrix [[A.sub.0]]

Given a polynomial p [element of] R, one can form a new ring R[prime] = R/p consisting of

cosets of polynomials, with members of the same

coset differing by multiples of p.

As for type II extensions N/Q, of degree [l.sup.N] say, one has H(N) = G and so Corollary 1.9 implies only that [Mathematical Expression Omitted] belongs to the

coset [Mathematical Expression Omitted] which has cardinality [l.sup.N-1] (cf.

If [GAMMA] acts on a homogeneous space G/H properly discontinuously and freely, then the double

coset space [GAMMA]\G/H has a natural manifold structure.

If R is the 8 element hunting group with I = (x14)[.sup.4], and I the group {I, bc, (bc)[.sup.2]}, then all but the last row of the three columns (Table 1) give the

coset decomposition [S.sub.4] = R + bc R + (bc)[.sup.2] R, while the first eight rows (Table 1) (of three elements each) represent the partition [S.sub.4] = I + I x + ...