Let H = (V, E) be a hypergraph, where V is set of vertices and E non-empty subsets called edges. If all edges have the same cardinality r, then an r-uniform hypergraph; if consists r-subsets V, complete denoted by $$K_n^r$$ , n |V|. A hypergraph H′ (V′, E′) subhypergraph V′ ⊆ E′ E. The edge-connectivity minimum edge F such that − not connected, F). An k-edge-maximal every has at most k, but for...

Let H be a closed, noncompact subgroup of a simple Lie group G, such that G/H admits an invariant Lorentz metric. We show that if G = SO(2, n), with n ≥ 3, then the identity component H of H is conjugate to SO(1, n). Also, if G = SO(1, n), with n ≥ 3, then H is conjugate to SO(1, n− 1).

We construct a finitely presented torsion-free simple group Σ0, acting cocompactly on a product of two regular trees. An infinite family of such groups has been introduced by Burger-Mozes ([2, 4]). We refine their methods and get Σ0 as an index 4 subgroup of a group Σ < Aut(T12)×Aut(T8) presented by 10 generators and 24 short relations. For comparison, the smallest virtually simple group of [4,...

We show that any non-zero orbit under a non-compact, simple, irreducible linear group is dense in the Bohr compactification of the ambient space.

Let G be a connected Lie group acting by algebra automorphisms on a finite-dimensional complex central simple algebra A. The algebra A is isomorphic to the endomorphism algebra of a projective representation V of G. We study the invariant subalgebras of A. In particular, we show that if V is irreducible, then the invariant subalgebras appear in dual pairs arising from factorizations of V . We a...

Simple finite group schemes over an algebraically closed field of positive characteristic p 6= 2, 3 have been classified. We consider the problem of determining their infinitesimal deformations. In particular, we compute the infinitesimal deformations of the simple finite group schemes of height one corresponding to the restricted simple Lie algebras.