Please use this identifier to cite or link to this item: http://hdl.handle.net/11452/25142
Title: Commutator subgroups of the extended Hecke groups (H)over-bar(lambda(q))
Authors: Şahin, Recep
Uludağ Üniversitesi/Fen-Edebiyat Fakültesi/Matematik Bölümü.
0000-0002-0700-5774
Bizim, Osman
Cangül, İsmail Naci
AAH-1468-2021
J-3505-2017
ABA-6206-2020
9245697900
57189022403
Keywords: Mathematics
Hecke group
Extended hecke group
Commutator subgroup
Issue Date: 2004
Publisher: Springer Heidelberg
Citation: Şahin, R. vd. (2004). “Commutator subgroups of the extended Hecke groups (H)over-bar(lambda(q))”. Czechoslovak Mathematical Journal, 54(1), 253-259.
Abstract: Hecke groups H(lambda(q)) are the discrete subgroups of PSL(2, R) generated by S(z) = -(z + lambda(q))(-1) and T(z) = -1/z. The commutator subgroup of H(lambda(q)), denoted by H'(lambda(q)), is studied in [2]. It was shown that H'(lambda(q)) is a free group of rank q - 1. Here the extended Hecke groups (H) over bar(lambda(q)), obtained by adjoining R-1(z) = 1/(z) over bar to the generators of H(lambda(q)), are considered. The commutator subgroup of (H) over bar(lambda(q)) is shown to be a free product of two finite cyclic groups. Also it is interesting to note that while in the H(lambda(q)) case, the index of H'(lambda(q)) is changed by q, in the case of (H) over bar(lambda(q)), this number is either 4 for q odd or 8 for q even.
URI: https://doi.org/10.1023/B:CMAJ.0000027265.81403.8d
https://link.springer.com/content/pdf/10.1023/B:CMAJ.0000027265.81403.8d.pdf
http://hdl.handle.net/11452/25142
ISSN: 0011-4642
Appears in Collections:Scopus
Web of Science

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