ﻻ يوجد ملخص باللغة العربية
We describe here the lower garland of some lattices of intermediate subgroups in linear groups. The results are applied to the case of subgroup lattices in general and special linear groups over a class of rings, containing the group of rational points T of a maximal non-split torus in the corresponding algebraic group. It turns out that these garlands coincide with the interval of the whole lattice, consisting of subgroups between T and its normalizer.
Let $F$ be any field. We give a short and elementary proof that any finite subgroup $G$ of $PGL(2,F)$ occurs as a Galois group over the function field $F(x)$. We also develop a theory of descent to subfields of $F$. This enables us to realize the aut
For a finite volume geodesic polyhedron P in hyperbolic 3-space, with the property that all interior angles between incident faces are integral submultiples of Pi, there is a naturally associated Coxeter group generated by reflections in the faces. F
A complete description of subgroups in the general linear group over a semilocal ring containing the group of diagonal matrices was obtained by Z.I.Borewicz and N.A.Vavilov. It is shown in the present paper that a similar description holds for the in
We develop tools for classification of contraction algebras and apply these to solve the problem on classification up to isomorphism of 8 and 9 dimensional algebras corresponding to 3-fold flops. We prove that there is only one up to isomorphism cont
This paper is a continuation of our article (European J. Math., https://doi.org/10.1007/s40879-020-00419-8). The notion of a poor complex compact manifold was introduced there and the group $Aut(X)$ for a $P^1$-bundle over such a manifold was proven