Sylow theory in locally finite groups
Sylow theory of -groups
Symmetric operations in groups
Symmetric words in nilpotent groups of class ≤ 3
System of equations in commuting variables for free products of Abelian groups.
Systems of equations over locally p-indicable groups.
Systolic invariants of groups and -complexes via Grushko decomposition
We prove a finiteness result for the systolic area of groups. Namely, we show that there are only finitely many possible unfree factors of fundamental groups of -complexes whose systolic area is uniformly bounded. We also show that the number of freely indecomposable such groups grows at least exponentially with the bound on the systolic area. Furthermore, we prove a uniform systolic inequality for all -complexes with unfree fundamental group that improves the previously known bounds in this dimension....
S-полные группы, SR- группы, SD- группы
-systems of finite simple groups
Tarski's problem about the elementary theory of free groups has a positive solution.
Term functions on non-Abelian groups of order
Test elements and test rank of a free metabelian group.
Test elements and the retract theorem in hyperbolic groups.
The 27-dimensional module for E6. I.
The absolute Galois group of a pseudo p-adically closed field.
The absolute Galois group of a pseudo real closed field
The accessibility of finitely presented groups.
The amalgamation basis of the category of compact groups.
The arithmetic of curves defined by iteration
We show how the size of the Galois groups of iterates of a quadratic polynomial f can be parametrized by certain rational points on the curves Cₙ: y² = fⁿ(x) and their quadratic twists (here fⁿ denotes the nth iterate of f). To that end, we study the arithmetic of such curves over global and finite fields, translating key problems in the arithmetic of polynomial iteration into a geometric framework. This point of view has several dynamical applications. For instance, we establish a maximality theorem...
The asymptotic dimension of the first Grigorchuk group is infinity.
We describe a sufficient condition for a finitely generated group to have infinite asymptotic dimension. As an application, we conclude that the first Grigorchuk group has infinite asymptotic dimension.