On some free groups, generated by matrices

Piotr Slanina

doi:10.1515/dema-2004-0107

On some free groups, generated by matrices

Piotr Slanina

Department of Mathematics (RMS/RMS1)

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

The interest to free groups generated by 2 × 2 matrices (Equation Presented) is known since 1947 when Sanov proved that for λ = 2 the group G_λ = gp(A_λ,C_λ) is a free group [22]. For |λ| ≥ 2 the proof of this fact can be found in [3], The aim of this paper is to show that if λ is outside of four unit circles |λ ± 1| ≥ 1 and |λ ± i| ≥ 1 then also G_λ is a free group.

Original language	English
Pages (from-to)	55-61
Number of pages	7
Journal	Demonstratio Mathematica
Volume	37
Issue number	1
DOIs	https://doi.org/10.1515/dema-2004-0107
Publication status	Published - Jan 2004

ASJC Scopus subject areas

General Mathematics

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abstract = "The interest to free groups generated by 2 × 2 matrices (Equation Presented) is known since 1947 when Sanov proved that for λ = 2 the group Gλ = gp(Aλ,Cλ) is a free group [22]. For |λ| ≥ 2 the proof of this fact can be found in [3], The aim of this paper is to show that if λ is outside of four unit circles |λ ± 1| ≥ 1 and |λ ± i| ≥ 1 then also Gλ is a free group.",

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AB - The interest to free groups generated by 2 × 2 matrices (Equation Presented) is known since 1947 when Sanov proved that for λ = 2 the group Gλ = gp(Aλ,Cλ) is a free group [22]. For |λ| ≥ 2 the proof of this fact can be found in [3], The aim of this paper is to show that if λ is outside of four unit circles |λ ± 1| ≥ 1 and |λ ± i| ≥ 1 then also Gλ is a free group.

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On some free groups, generated by matrices

Abstract

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