Abstract
This paper is tightly connected with the book [Varieties of Group Representations. General Theory, Connections and Applications (Zinatne, Riga, 1983) (in Russian)]. In the paper we prove new results in the spirit of the above-mentioned book. They are related to dimension subgroups, varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of associative algebras. We provide the reader with the list of open problems. For many reasons we consciously included in the text a brief review of the basic definitions and results from the theory of varieties of representations described in the book [Varieties of Group Representations. General Theory, Connections and Applications].
| Original language | English |
|---|---|
| Pages (from-to) | 1149-1178 |
| Number of pages | 30 |
| Journal | International Journal of Algebra and Computation |
| Volume | 21 |
| Issue number | 7 |
| DOIs | |
| State | Published - Nov 2011 |
Bibliographical note
Funding Information:We are very thankful to anonymous referee of the paper for introducing the definition of a residually PI-group. We are grateful to M. Bestvina and M. Sapir for pointing out the fact that the groups of outer automorphisms of free groups Fn, n > 3 have no nilpotent normal subgroups. E. Aladova was supported by the Minerva foundation through the Emmy Noether Research Institute, by the Israel Science Foundation grant number 1178/06 and ISF center of excellence 1691/10. The support of these institutions is gratefully appreciated.
Keywords
- PI-group
- Variety of representations of groups
- dimension subgroups
- semigroup of varieties of representations of groups
- variety of associative algebras