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

Magalyas, L. K.

Mat. Issled. 103, 104-121 (1988).

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

MSC:

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

Keywords:

point symmetry group; subdirect product