Surjectivity of certain word maps on PSL(2,C) and SL(2,C)

Let n ⩾ 2 be an integer and F n the free group on n generators, its first and second derived subgroups. Let K be an algebraically closed field of characteristic zero. We show that if , then the corresponding word map is surjective. We also describe certain word maps that are surjective on SL ( 2 , C...

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Bibliographic Details
Published in:	European journal of mathematics Vol. 2; no. 3; pp. 614 - 643
Main Authors:	Bandman, Tatiana, Zarhin, Yuri G.
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-09-2016 Springer Nature B.V
Subjects:	Algebraic Geometry Mathematics Mathematics and Statistics Research Article Subgroups 20G20 14L24 14L35 20E32 Magnus embedding 14L10 Word map Special linear group 20F70 Trace map 20F14 20F45
Online Access:	Get full text
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Summary:	Let n ⩾ 2 be an integer and F n the free group on n generators, its first and second derived subgroups. Let K be an algebraically closed field of characteristic zero. We show that if , then the corresponding word map is surjective. We also describe certain word maps that are surjective on SL ( 2 , C ) .
ISSN:	2199-675X 2199-6768
DOI:	10.1007/s40879-016-0101-9