On the some normal subgroups of the extended modular group

Şahіn, Recep

doi:10.1016/j.amc.2011.03.074

Cited by 4 publications

(3 citation statements)

References 7 publications

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“…His results have been generalized to Hecke groups H (λ q ), by Cangül and Singerman for q ≥ 3 prime in [1], by Ikikardes, Koruoglu and Sahin for q ≥ 4 even integer in [7] and by Cangül, Sahin, Ikikardes and Koruoglu for q ≥ 3 odd integer in [2]. For q ≥ 3 prime, the power subgroups of the extended Hecke groups H (λ q ) were studied by Sahin, Ikikardes and Koruoglu in [15,16] and [17].…”

Section: Introductionmentioning

confidence: 95%

Commutator subgroups of the power subgroups of some Hecke groups

Şahіn

Koruoğlu

2010

Ramanujan J

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Let q ≥ 3 be a prime and let H (λ q ) be the Hecke group associated to q. Let m be a positive integer and H m (λ q ) be the mth power subgroup of H (λ q ). In this work, we study the commutator subgroups of the power subgroups H m (λ q ) of H (λ q ). Then, we give the derived series for all triangle groups of the form (0; 2, q, n) for n a positive integer, since there is a nice connection between the signatures of the subgroups we studied and the signatures of these derived series.

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Section: Introductionmentioning

confidence: 95%

Commutator subgroups of the power subgroups of some Hecke groups

Şahіn

Koruoğlu

2010

Ramanujan J

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“…< ∞, 0, NBRF for parabolic element f.h 2 .f 2 .h.f.h 2 .f.T W(U,T) for reflection element T.U −2 .T.U 3 .T.R.T.U.T.U −3 .T.U 2 .T BRF for reflection element T S 2 2 . (T S) 3 . T S 2 .…”

Section: Pathmentioning

confidence: 99%

Farey graph and rational fixed points of the extended modular group

Demır

Karataş

2022

Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat.

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Fixed points of matrices have many applications in various areas of science and mathematics. Extended modular group ¯¯¯¯ΓΓ¯ is the group of 2×22×2 matrices with integer entries and determinant ±1±1. There are strong connections between extended modular group, continued fractions and Farey graph. Farey graph is a graph with vertex set ^Q=Q∪{∞}Q^=Q∪{∞}. In this study, we consider the elements in ¯¯¯¯ΓΓ¯ that fix rationals. For a given rational number, we use its Farey neighbours to obtain the matrix representation of the element in $\overline{\Gamma}$ that fixes the given rational. Then we express such elements as words in terms of generators using the relations between the Farey graph and continued fractions. Finally we give the new block reduced form of these words which all blocks have Fibonacci numbers entries.

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“…We know from [37] that the subgroup (H 2 ) ′ (λ 3 ) is equal to the congruence subgroup H 4 (λ 3 ). We want to derive a similar equation for H(λ 5 ).…”

Section: Of Course If We Know the Generators Of Any One Of These Submentioning

confidence: 99%

Some results on Hecke and extended Hecke groups

Şahіn¹

2018

Turk J Math

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Let q ≥ 3 be a prime number and let H(λq) be the extended Hecke group associated with q. In this paper, we determine the presentation of the commutator subgroup ( H ( λq)α) ′ of the normal subgroup H ( λq)α , where H ( λq)α is a subgroup of index 2 in H ( λq). Next we discuss the commutator subgroup ( H2) ′ ( λq) of the principal congruence subgroup H2 ( λq) of H ( λq) . Then we show that some quotient groups of H ( λq) are generalized M * − groups. Finally, we prove some results related to some normal subgroups of H ( λq) , especially in the case q = 5.

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On the some normal subgroups of the extended modular group

Cited by 4 publications

References 7 publications

Commutator subgroups of the power subgroups of some Hecke groups

Commutator subgroups of the power subgroups of some Hecke groups

Farey graph and rational fixed points of the extended modular group

Some results on Hecke and extended Hecke groups

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