Point symmetry groups with invariant nondegenerate planes in the space \(^ 2{\mathbb{R}}_ 4\). (Russian) Zbl 0669.51016

Let G be a point symmetry group of the space \(^ 2{\mathbb{R}}_ 4\) which leaves invariant two absolutely perpendicular nondegenerate planes of this space. These planes are of one of the following types: \({\mathbb{R}}_ 2\), \(^ 2{\mathbb{R}}_ 2\), or \(^ 1{\mathbb{R}}_ 2\). Let \(G_ 1\) and \(G_ 2\) be the projections of G upon these planes. Then G can be constructed as a subdirect product of the groups \(G_ 1\) and \(G_ 2\). The purpose of this paper is to investigate all possibilities for such a subdirect product.
Reviewer: A.Kontrat’ev


51M10 Hyperbolic and elliptic geometries (general) and generalizations
20H15 Other geometric groups, including crystallographic groups
51F15 Reflection groups, reflection geometries
20E22 Extensions, wreath products, and other compositions of groups
Full Text: EuDML