We study real hypersurfaces of a complex space form Mn(c), c ≠ 0 under certain conditions of the Ricci tensor on the orthogonal distribution T0.

This note contains the classification of the finite groups G satisfying the condition NG(H)/CG(H) ≅ Aut(H) for every abelian subgroup H of G.

It is shown that if f is an entire transcendental function, l a straight line in the complex plane, and n ≥ 2, then f has infinitely many repelling periodic points of period n that do not lie on l.

In this paper we study the topology of the space of harmonic maps from S2 to ℂℙ2.We prove that the subspaces consisting of maps of a fixed degree and energy are path connected. By a result of Guest and Ohnita it follows that the same is true for the space of harmonic maps to ℂℙn for n ≥ 2. We show that the components of maps to ℂℙ2 are complex manifolds.

A general lacunary Littlewood-Paley type theorem is proved, which applies in a variety of settings including Jacobi polynomials in [0, 1], SU(2), and the usual classical trigonometric series in [0, 2π). The theoremis used to derive new results for Lp multipliers on SU(2) and Jacobi Lp multipliers.

Let A be a finite abelian group and M be a branched cover of an homology 3-sphere, branched over a link L, with covering group A. We show that H1(M; Z[1/|A|]) is determined as a Z[1/|A|][A]-module by the Alexander ideals of L and certain ideal class invariants.

Criteria for local uniform rotundity and midpoint local uniform rotundity in Orlicz-Lorentz spaces with the Luxemburg norm are given. Strict K-monotonicity and Kadec-Klee property are also discussed.

We show that if A is a torsion-free word hyperbolic group which belongs to class (Q), that is all finitely generated subgroups of A are quasiconvex in A, then any maximal cyclic subgroup U of A is a Burns subgroup of A. This, in particular, implies that if B is a Howson group (that is the intersection of any two finitely generated subgroups is finitely generated) then A *UB, ⧼A, t | Ut = V⧽ are also Howson groups. Finitely generated free groups, fundamental groups of closed hyperbolic surfaces and some interesting 3-manifold groups are known to belong to class (Q) and our theorem applies to them. We also describe a large class of word hyperbolic groups which are not Howson.

The main purpose of this paper is to study groups G1, G2 such that H*(BG1, Z/p) is isomorphic to H*(BG2, Z/p) in U, the category of unstable modules over the Steenrod algebra A, but not isomorphic as graded algebras over Z/p.

Using naive algebraic geometric methods a new proof of the following celebrated theorem of Magnus is given: Let G be a group with a presentation having n generators and m relations. If G also has a presentation on n − m generators, then G is free of rank n − m.

In this paper, we consider Dirichlet series with Euler products of the form F(s) = Πp in > 1, and which are regular in ≥ 1 except for a pole of order m at s = 1. We establish criteria for such a Dirichlet series to be nonvanishing on the line of convergence. We also show that our results can be applied to yield non-vanishing results for a subclass of the Selberg class and the Sato-Tate conjecture.

We classify the compact 3-manifolds whose boundary is a union of 2-spheres, and which embed in T ×I ×I, where T is a triod and I the unit interval. This class is described explicitly as the set of punctured handlebodies. We also show that any 3-manifold in T × I × I embeds in a punctured handlebody.

Let H be the split, adjoint group of type E6 over a p-adic field. In this paper we study the restriction of the minimal representation of H to the closed subgroup PGL3 × G2.