22 citations · 63 across the 19 of their papers we have counts for
6 papers · 1 filter
Surjectivity of certain word maps on PSL(2,C) and SL(2,C)
Tatiana Bandman, Yuri G. Zarhin
We show that an element w of a free group F on n generators defines a surjective word map of PSL(2,C)^n onto PSL(2,C) unless w belongs to the second derived subgroup of F. We also…
Criteria for equidistribution of solutions of word equations on SL(2)
Tatiana Bandman, Boris Kunyavskii
We study equidistribution of solutions of word equations of the form w(x,y)=g in the family of finite groups SL(2,q). We provide criteria for equidistribution in terms of the trace…
Surjectivity and equidistribution of the word x^ay^b on PSL(2,q) and SL(2,q)
Tatiana Bandman, Shelly Garion
We determine the positive integers a,b and the prime powers q for which the word map w(x,y)=x^ay^b is surjective on the group PSL(2,q) (and SL(2,q)). We moreover show that this map…
On the Surjectivity of Engel Words on PSL(2,q)
Tatiana Bandman, Shelly Garion, Fritz Grunewald
We investigate the surjectivity of the word map defined by the n-th Engel word on the groups PSL(2,q) and SL(2,q). For SL(2,q), we show that this map is surjective onto the subset…
Engel-like characterization of radicals in finite dimensional Lie algebras and finite groups
Tatiana Bandman, Mikhail Borovoi, Fritz Grunewald +2
A classical theorem of R. Baer describes the nilpotent radical of a finite group G as the set of all Engel elements, i.e. elements y in G such that for any x in G the n-th commutat…
Engel-like Identities Characterizing Finite Solvable Groups
Tatiana Bandman, Gert-Martin Greuel, Fritz Grunewald +3
In the paper we characterize the class of finite solvable groups by two-variable identities in a way similar to the characterization of finite nilpotent groups by Engel identities.…