We say that the width of an infinite subgroup H in G is n if there exists a collection of n essentially distinct conjugates of H such that the intersection of any two elements of the collection is infinite and n is maximal possible. We define the width of a finite subgroup to be 0. We prove that a quasiconvex subgroup of a negatively curved group has finite width. It follows that geometrically ...

Hart, K.P. and J. van Mill, Discrete sets and the maximal totally bounded group topology, Journal of Pure and Applied Algebra 70 (1991) 73-80. If G is an Abelian group, then G # is G with its maximal totally bounded group topology. We prove that every A c G# contains a closed (in G#) and discrete subset B such that lB1 = IAl. This answers a question posed by Eric van Douwen. We also present an ...

A group G is simple if and only if the diagonal subgroup of G ×G is a maximal subgroup. This striking property is very easy to prove and raises the question of determining all the maximal subgroups of G , where G denotes the direct product of n copies of G . The first purpose of this note is to answer completely this question. We show in particular that if G is perfect, then any maximal subgrou...

The problem of the maximal size of cap sets is a characteristic 3 model for the problem of finding arithmetic progressions of length 3 in rather dense sets of integers. Meshulam [M95] , through a direct use of ideas of Roth, was able to show that there is a constant C so that any cap set A has density at most C N . Our result may be viewed as a very modest improvement over Meshulam’s result. Sa...

In this paper we find trees with minimal and maximal MerrifieldSimmons index over the set Ω (n, 2) of all trees with n vertices and 2 branching vertices, and also over the subset Ω (n, 2) of all trees in Ω (n, 2) such that the branching vertices are connected by the path Pt.

We extend the domain of preferences to include menu-dependent preferences and characterize the maximal subset of this domain in which the revelation principle holds. Minimax-regret preference is shown to be outside this subset.

We establish sufficient conditions for the appearance of both apparent horizons and singularities in spherically symmetric initial data when spacetime is foliated extrinsically. Let M and P be respectively the total material energy and the total material current contained in some ball of radius `. Suppose that the dominant energy condition is satisfied. We show that if M − P ≥ ` then the region...

Let (A, m, k) be a complete intersection of codimension c, and k̃ the algebraic closure of k. We show that every homogeneous algebraic subset of k̃c is the cohomological support variety of an A-module, and that the projective variety of a complete indecomposable maximal Cohen-Macaulay A-module is connected.

The positive mass theorem of general relativity to be addressed here states that the total mass of an isolated gravitational system (viewed from spatial infinity, known as the ADM mass) must be non-negative if its local mass density is non-negative everywhere, and in fact the mass is strictly positive unless the space-time is flat. In this essay we are only concerned with the first part of this...

Let K be a field of characteristic 6= 2, let Br(K)2 be the 2primary part of its Brauer group, and let GK(2) = Gal(K(2)/K) be the maximal pro-2 Galois group of K. We show that Br(k)2 is a finite elementary abelian 2-group (Z/2Z), r ∈ N, if and only if GK(2) is a free pro-2 product of a closed subgroup H which is generated by involutions and of a free pro-2 group. Thus, the fixed field of H in K(...