Word maps on perfect algebraic groups

Nikolai Gordeev, Boris Kunyavskiǐ, Eugene Plotkin

Research output: Contribution to journalArticlepeer-review

11 Scopus citations

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 languageEnglish
Pages (from-to)1487-1515
Number of pages29
JournalInternational Journal of Algebra and Computation
Volume28
Issue number8
DOIs
StatePublished - 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).

FundersFunder number
Emmy Noether Research Institute for Mathematics
Ministry of Education and Science of the Russian Federation1.661.2016/1.4
Israel Science Foundation1623/16

    Keywords

    • Word map
    • linear algebraic group
    • perfect group

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