On some free groups, generated by matrices

Piotr Slanina

doi:10.1515/dema-2004-0107

On some free groups, generated by matrices

Piotr Slanina

Katedra Matematyki (RMS/RMS1)

Wyniki badań: Wkład do czasopisma › Artykuł › recenzja

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Abstrakt

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.

Język oryginału	angielski
Strony (od–do)	55-61
Liczba stron	7
Czasopismo	Demonstratio Mathematica
Tom	37
Numer wydania	1
Identyfikatory DOI	https://doi.org/10.1515/dema-2004-0107
Status publikacji	Opublikowano - sty 2004

Obszary tematyczne ASJC Scopus

Matematyka ogólna

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10.1515/dema-2004-0107

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Cytowanie

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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

Abstrakt

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