9 citations · 10 across the 6 of their papers we have counts for
8 papers
Double cosets of normalizers of maximal tori of simple algebraic groups and orbits of partial actions of Cremona subgroups
N. Gordeev, E. Egorchenkova
Let be a simple algebraic group over an algebraically closed field and let be the normalizer of a fixed maximal torus . Further, let be the unipot…
Geometry of word equations in simple algebraic groups over special fields
Nikolai Gordeev, Boris Kunyavskii, Eugene Plotkin
This paper contains a survey of recent developments in investigation of word equations in simple matrix groups and polynomial equations in simple (associative and Lie) matrix algeb…
Word maps on perfect algebraic groups
Nikolai Gordeev, Boris Kunyavskii, Eugene Plotkin
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 w…
Word maps, word maps with constants and representation varieties of one-relator groups
Nikolai Gordeev, Boris Kunyavskii, Eugene Plotkin
We consider word maps and word maps with constants on a simple algebraic group. We present results on the images of such maps, in particular, we prove a theorem on the dominance of…
Equations in simple Lie algebras
Tatiana Bandman, Nikolai Gordeev, Boris Kunyavskii +1
Given an element of the finitely generated free Lie algebra, for any Lie algebra we can consider the induced polynomial map . Assuming that is…
From Thompson to Baer-Suzuki: a sharp characterization of the solvable radical
Nikolai Gordeev, Fritz Grunewald, Boris Kunyavskii +1
We prove that an element of prime order belongs to the solvable radical of a finite (or, more generally, a linear) group if and only if for every the subgr…