Sylow 2-subgroups of the periodic groups saturated with finite simple groups

We prove that every 2-subgroup of a periodic group saturated with groups of Lie type over fields of odd characteristics whose Lie ranks are bounded as a whole is Chernikov. In particular, every such group is locally finite.     

Finite groups with special Sylow 2-subgroups

Let T be a Sylow 2-subgroup of a simple group PSU (3, 2ⁿ), and Z a proper subgroup belonging to the center of T. We shall prove that a simple finite group whose Sylow 2-subgroup is isomorphic to T/Z coincides with PSU (3, 2ⁿ). As a consequence we list simple groups that can be represented in the form of a product of two Schmidt groups, i.e., of minimal nonnilpotent groups.Translated from Matematicheskie Zametki, Vol. 14, No. 2, pp. 217–222, August, 1973.     

On finite groups with special Sylow <Emphasis Type=Italic>p</Emphasis>-subgroups

We find the cases in which a finite p-soluble group with a special Sylow p-subgroup has p-length 1.     

On intersections of Sylow 2-subgroups in automorphism groups of finite simple groups of exceptional Lie type

We consider the problem of interpolation of finite sets of numerical data bounded in L _p -norms (1 ≤ p < ∞) by smooth functions that are defined in an n-dimensional Euclidean ball of radius R and vanish on the boundary of the ball. Under some constraints on the location of interpolation nodes, we obtain two-sided estimates with a correct dependence on R for the L _p -norms of the Laplace operators of the best interpolants.     

Sylow 2-subgroups of rational solvable groups

A long-standing conjecture proposes that a Sylow 2-subgroup S of a finite rational group must be rational. In this paper we provide a counterexample to this conjecture, but we show that if G is solvable and S has nilpotence class 2, then S actually is rational.     

Simple modules for groups with abelian Sylow 2-subgroups are algebraic

An algebraic module is a KG-module that satisfies a polynomial with integer coefficients, with addition and multiplication given by direct sum and tensor product. In this article we prove that if G is a group with abelian Sylow 2-subgroups and K is a field of characteristic 2, then every simple KG-module is algebraic.