# coset

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## coset

[′kō‚set]
(mathematics)
For a subgroup of a group, a set consisting of all elements of the form xh or of all elements of the form hx, where h is an element of the subgroup and x is a fixed element of the group.
References in periodicals archive ?
We choose a normal subgroup [GAMMA]' [??] [GAMMA] of finite index that has no elliptic point nor irregular cusp.
where [??] and [??] are taken for every finite index set K such that [lambda] = [[??].sub.i[member of]K][[lambda].sub.i], respectively.
Comparing homomorphisms into H I An with homomorphisms into H [??] [S.sub.n] gives information on the embedding of finite index subgroups in large groups.
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.
Now the general case for finite index to prove that K is a field follows as in [6].
Since A is finitely generated torsion-free abelian, C is a direct factor of a subgroup [A.sub.1] of A of finite index; that is, [A.sub.1] = C X H, where [A : [A.sub.1]] = n < [infinity].
Moreover, the tower !G.sub.k^ = !(!summation of^X).sub.k^, !S.sup.!n.sub.!Alpha^^^ has the property that for each k, the image of !G.sub.k+1^ has finite index in !G.sub.k^.
For any field L with F [subset] L [subset] [??], the group G(L) is a discrete subgroup of G([A.sub.L]) if and only if A(K) [subset] A(L) is of finite index.
Secondly, if C is a subfactor of finite index in M, then its center is atomic, but its relative commutant is finite dimensional.
In this paper we deal only with regular languages, for which [[less than or equal to].sub.L] has finite index. The reason is that for a regular language L there are only finitely many languages of the form [x.sup.-1] [Ly.sup.-1] = {u [member of] [A.sup.*] | xuy [member of] L}.
Then [G'.sub.0] is a finite index solvable normal subgroup of G'.
If G is infinite amenable group and H contains a finite index normal subgroup N with N [intersection] A = {1}, then (G, H, A) [member of] A'.

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