Nilpotent-by-finite groups with isomorphic finite quotients

Quotients of adic spaces by finite groups

We prove that if X is an analytic adic space with an action of a finite group G, a categorical adic space quotient X/G exists under a mild hypothesis, in analogy with a classical result for schemes. We also show that if X is perfectoid, then X/G is perfectoid in many cases.

Determining Fuchsian groups by their finite quotients

Let C(Γ) be the set of isomorphism classes of the finite groups that are quotients (homomorphic images) of Γ. We investigate the extent to which C(Γ) determines Γ when Γ is a group of geometric interest. If Γ1 is a lattice in PSL(2,R) and Γ2 is a lattice in any connected Lie group, then C(Γ1) = C(Γ2) implies that Γ1 ∼= Γ2. If F is a free group and Γ is a right-angled Artin group or a residually...

Torus quotients as global quotients by finite groups

This article is motivated by the following local-to-global question: is every variety with tame quotient singularities globally the quotient of a smooth variety by a finite group? We show that this question has a positive answer for all quasi-projective varieties which are expressible as a quotient of a smooth variety by a split torus (e.g. simplicial toric varieties). Although simplicial toric...

NILPOTENT p-LOCAL FINITE GROUPS

In this paper we provide characterizations of p-nilpotency for fusion systems and p-local finite groups that are inspired by known result for finite groups. In particular, we generalize criteria by Atiyah, Brunetti, Frobenius, Quillen, Stammbach and Tate.

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup