Bounds on the torsion subgroups of Néron–Severi groups

On Torsion Subgroups of Lie Groups

We are concerned with torsion subgroups of Lie groups. We extend the classical result of C. Jordan on the structure of finite linear groups to torsion subgroups of connected Lie groups. 1. In [1], Boothby and Wang proved that, for any connected Lie group G, there exists a number k{G) such that any finite subgroup contains an abelian normal subgroup whose index is bounded by k{G), thereby genera...

Surface Subgroups of Kleinian Groups with Torsion

A subgroup of a group is known as a surface subgroup if it is isomorphic to the fundamental group of a closed connected orientable surface with positive genus. The surface subgroup conjecture in low-dimensional topology proposes that if the fundamental group of a closed orientable irreducible 3-manifold is infinite, then it contains a surface subgroup. With the recent solution to the geometrisa...

On Torsion Subgroups in Integral Group Rings of Finite Groups

Bounds for the `-torsion in Class Groups

We prove for each integer ` ≥ 1 an unconditional upper bound for the size of the `-torsion subgroup ClK [`] of the class group of K, which holds for all but a zero density set of number fields K of degree d ∈ {4, 5} (with the additional restriction in the case d = 4 that the field be non-D4). For sufficiently large ` this improves recent results of Ellenberg, Matchett Wood, and Pierce, and is a...

The Two - Generator Subgroups of One - Relator Groups with Torsion

The main aim of this paper is to show that every two-generator subgroup of any one-relator group with torsion is either a free product of cyclic groups or is a one-relator group with torsion. This result is proved by using techniques for reducing pairs of elements in certain HNN groups. These techniques not only apply to one-relator groups with torsion but also to a large number of other groups...