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

Tatiana Bandman; Yuri G. Zarhin

doi:10.1007/s40879-016-0101-9

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

Tatiana Bandman, Yuri G. Zarhin

Mathematics

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13 Scopus citations

Abstract

Let n⩾ 2 be an integer and F_n the free group on n generators, [InlineEquation not available: see fulltext.] its first and second derived subgroups. Let K be an algebraically closed field of characteristic zero. We show that if [InlineEquation not available: see fulltext.], then the corresponding word map [InlineEquation not available: see fulltext.] is surjective. We also describe certain word maps that are surjective on SL (2 , C).

Original language	English (US)
Pages (from-to)	614-643
Number of pages	30
Journal	European Journal of Mathematics
Volume	2
Issue number	3
DOIs	https://doi.org/10.1007/s40879-016-0101-9
State	Published - Sep 1 2016

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s40879-016-0101-9

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abstract = "Let n⩾ 2 be an integer and Fn the free group on n generators, [InlineEquation not available: see fulltext.] its first and second derived subgroups. Let K be an algebraically closed field of characteristic zero. We show that if [InlineEquation not available: see fulltext.], then the corresponding word map [InlineEquation not available: see fulltext.] is surjective. We also describe certain word maps that are surjective on SL (2 , C).",

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AU - Bandman, Tatiana

AU - Zarhin, Yuri G.

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N2 - Let n⩾ 2 be an integer and Fn the free group on n generators, [InlineEquation not available: see fulltext.] its first and second derived subgroups. Let K be an algebraically closed field of characteristic zero. We show that if [InlineEquation not available: see fulltext.], then the corresponding word map [InlineEquation not available: see fulltext.] is surjective. We also describe certain word maps that are surjective on SL (2 , C).

AB - Let n⩾ 2 be an integer and Fn the free group on n generators, [InlineEquation not available: see fulltext.] its first and second derived subgroups. Let K be an algebraically closed field of characteristic zero. We show that if [InlineEquation not available: see fulltext.], then the corresponding word map [InlineEquation not available: see fulltext.] is surjective. We also describe certain word maps that are surjective on SL (2 , C).

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

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