Deformation theory and finite simple quotients of triangle groups I

On Simple Groups of Finite Order. I

-distortion of Finite Quotients of Amenable Groups

We study the Lp-distortion of finite quotients of amenable groups. In particular, for every 2 ≤ p < ∞, we prove that the lp-distortions of the groups C2 ≀Cn and Cpn ⋉Cn are in Θ((log n) 1/p), and that the lp-distortion of C2 n ⋉A Z, where A is the matrix (

Finite Permutation Groups and Finite Simple Groups

In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both wi...

Quotients in Simple Type Theory

We introduce a syntax for quotient types in a predicate logic over a simply type theory. To illustrate its usefulness we construct in purely type theoretic terms (a) the free abelian group on a commutative monoid H, as quotient of H H; a special instance is the construction of Z from N; (b) the quotient poset of a preorder, (c) the abelian quotient of an arbitrary group, and (d) tensor products...

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.