The operators on Lp = Lp[0, 1], 1 ≤ p < ∞, which are not commutators are those of the form λI + S where λ , 0 and S belongs to the largest ideal in L(Lp). The proof involves new structural results for operators on Lp which are of independent interest.

SO(3) it is the proper symmetry group of the icosahedron (and the dodecahedron). It is the unique finite subgroup of SO(3) which equals its own commutator subgroup—in fact, it is the unique non-abelian simple finite subgroup of SO(3). It can be thought of as the beginning or smallest member of the family of non-abelian finite simple groups. From the point of view of the McKay correspondence it ...

In the present paper, we study the group SL 2 (H Z) of (2 2)-matrices with reduced norm 1 over the noncommutative ring of Hamilton quaternions with integral coeecients. In section 1, we obtain a presentation for SL 2 (H Z) in terms of generators and deening relations. In section 2, we exhibit a subgroup of nite index of SL 2 (H Z) with a nonabelian free quotient of rank 3. It is well known that...

This paper investigates ways to enlarge the Hamiltonian subgroup Ham of the symplectomorphism group Symp(M) of the symplectic manifold (M,ω) to a group that both intersects every connected component of Symp(M) and characterizes symplectic bundles with fiber M and closed connection form. As a consequence, it is shown that bundles with closed connection form are stable under appropriate small per...

We clarify the relationship between the linear commutator and the ordinary commutator by showing that in any variety satisfying a nontrivial idempotent Mal’cev condition the linear commutator is definable in terms of the centralizer relation. We derive from this that abelian algebras are quasi–affine in such varieties. We refine this by showing that if A is an abelian algebra and V(A) satisfies...

In this paper, we give the complete characterization of the p–torsion subgroups of certain idèle–class groups associated to characteristic p function fields. As an application, we answer a question which arose in the context of Tan’s approach [Ta1] to an important particular case of a generalization of a conjecture of Gross [Gro] on special values of L–functions. 1. Notation and motivation Let ...

We consider acyclic groups of low dimension. To indicate our results simply, let G′ be the nontrivial perfect commutator subgroup of a finitely presentable group G. Then def(G) ≤ 1. When def(G) = 1, G′ is acyclic provided that it has no integral homology in dimensions above 2 (a sufficient condition for this is that G′ be finitely generated); moreover, G/G′ is then Z or Z. Natural examples are ...