Abstract
We extend Borel's theorem on the dominance of word maps from semisimple algebraic groups to some perfect groups. In another direction, we generalize Borel's theorem to some words with constants. We also consider the surjectivity problem for particular words and groups, give a brief survey of recent results, present some generalizations and variations and discuss various approaches, with emphasis on new ideas, constructions and connections.
Original language | English |
---|---|
Pages (from-to) | 1487-1515 |
Number of pages | 29 |
Journal | International Journal of Algebra and Computation |
Volume | 28 |
Issue number | 8 |
DOIs | |
State | Published - 1 Dec 2018 |
Bibliographical note
Publisher Copyright:© 2018 World Scientific Publishing Company.
Funding
We thank the referees for careful reading and thoughtful remarks, which were very helpful for improving the original version. The research of the first author was financially supported by the Ministry of Education and Science of the Russian Federation, Project 1.661.2016/1.4. The research of the second and third authors was supported by ISF Grant 1623/16 and the Emmy Noether Research Institute for Mathematics. The paper was finished when the second author visited the MPIM (Bonn).
Funders | Funder number |
---|---|
Emmy Noether Research Institute for Mathematics | |
Ministry of Education and Science of the Russian Federation | 1.661.2016/1.4 |
Israel Science Foundation | 1623/16 |
Keywords
- Word map
- linear algebraic group
- perfect group