On trigonometries of finite groups and groups with subgroups having trigonometries (Q1358076)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On trigonometries of finite groups and groups with subgroups having trigonometries |
scientific article; zbMATH DE number 1023974
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On trigonometries of finite groups and groups with subgroups having trigonometries |
scientific article; zbMATH DE number 1023974 |
Statements
On trigonometries of finite groups and groups with subgroups having trigonometries (English)
0 references
22 June 1998
0 references
The author continues studying trigonometries of groups on exact pseudoplanes started in his papers [Model theory, Proc. Sov.-Fr. Colloq., Karaganda/USSR 1990, 185-201 (1990; Zbl 0755.03019) and Sib. Mat. Zh. 36, No. 2, 419-431 (1995; Zbl 0863.51010)]. New examples of trigonometries of finite groups and groups without trigonometries on projective planes are constructed. It is proved that if a subgroup of a group has a trigonometry then the group has a trigonometry. In particular, the existence of trigonometries for groups containing elements of order 2, 3, or \(\infty\) is proved. It is proved that every group can be embedded in some group with a trigonometry on a projective plane.
0 references
projective planes
0 references
exact pseudoplanes
0 references
trigonometries of groups
0 references
embeddings
0 references
existence
0 references
