Related papers: A Fitting Theorem for Simple Theories

We consider factorizations of a finite group $G$ into conjugate subgroups, $G=A^{x_{1}}\cdots A^{x_{k}}$ for $A\leq G$ and $x_{1},\ldots ,x_{k}\in G$, where $A$ is nilpotent or solvable. First we exploit the split $BN$-pair structure of…

It is shown that the classification theorems for semisimple algebraic groups in characteristic zero can be derived quite simply and naturally from the corresponding theorems for Lie algebras by using a little of the theory of tensor…

We make available some results about model theory cyclically ordered groups. We start with a classification of complete theories of divisible abelian cyclically ordered groups. Then we look at the cyclically ordered groups where the only…

In this paper we study analogues of amenability for topological groups in the context of definable structures. We prove fixed point theorems for such groups. More importantly, we propose definitions for definable actions and continuous…

Answering a special case of a question of Chernikov and Simon, we show that any non-dividing formula over a model M in a distal NIP theory is a member of a consistent definable family, definable over M.

We study infinite groups interpretable in power bounded $T$-convex, $V$-minimal or $p$-adically closed fields. We show that if $G$ is an interpretable definably semisimple group (i.e., has no definable infinite normal abelian subgroups)…

Word maps provide a wealth of information about finite groups. We examine the connection between the probability distribution induced by a word map and the underlying structure of a finite group. We show that a finite group is nilpotent if…

A derived version of Maschke's theorem for finite groups is proved: the derived categories, bounded or unbounded, of all blocks of the group algebra of a finite group are simple, in the sense that they admit no nontrivial recollements. This…

A remarkable result of Thompson states that a finite group is soluble if and only if its two-generated subgroups are soluble. This result has been generalized in numerous ways, and it is in the core of a wide area of research in the theory…

This paper studies effective separability for subgroups of finitely generated nilpotent groups and more broadly effective subgroup separability of finitely generated nilpotent groups. We provide upper and lower bounds that are polynomial…

The method of little groups describes the irreducible characters of semidirect products with abelian normal subgroups in terms of the irreducible characters of the factor groups. We modify this method to construct supercharacter theories of…

In this note we determine the finite groups that can be written as the union of any three irredundant/distinct proper subgroups. The finite groups that can uniquely be written as the union of three proper subgroups are also characterized.

We describe the structure of finite groups with $\mathfrak{F}$-subnormal or self-normalizing primary cyclic subgroups when $\mathfrak{F}$ is a subgroup-closed saturate superradical formation containing all nilpotent groups. We prove that…

This paper is about the $dfg$/$fsg$ decomposition for groups $G$ definable in $p$-adically closed fields. It is proved that for $G$ definably amenable, $G$ has a definable normal $dfg$ subgroup $H$ such that the quotient $G/H$ is a…

We survey some results on the structure of the groups which are definable in theories of fields involved in the applications of model theory to Diophantine geometry. We focus more particularly on separably closed fields of finite degree of…

We define simple tilings in the general context of a $G$-tiling on a Riemannian homogeneous space $M$ to be tilings by Riemannian simplices. As evidence that this definition is natural, we prove that a large class of tilings of $M$ are MLD…

In this paper, the Identity Problem for certain groups, which asks if the subsemigroup generated by a given finite set of elements contains the identity element, is related to problems regarding ordered groups. Notably, the Identity Problem…

We study infinite approximate subgroups of soluble Lie groups. Generalising a theorem of Fried and Goldman we show that approximate subgroups are close, in a sense to be defined, to genuine connected subgroups. Building up on this result we…

Simple type theory is formulated for use with the generic theorem prover Isabelle. This requires explicit type inference rules. There are function, product, and subset types, which may be empty. Descriptions (the eta-operator) introduce the…

Let $A$ and $G$ be finite groups such that $A$ acts coprimely on $G$ by automorphisms, assume that $G$ has a maximal $A$-invariant subgroup $M$ that is a direct product of some isomorphic simple groups, we prove that if $G$ has a…