Power and free normal subgroups of generalized Hecke groups

2019 ◽  
Vol 13 (04) ◽  
pp. 2050080
Author(s):  
Recep Sahin ◽  
Taner Meral ◽  
Özden Koruoğlu
Keyword(s):  
Positive Integer ◽  
Normal Subgroups ◽  
Hecke Groups ◽  
Hecke Group

Let [Formula: see text] and [Formula: see text] be integers such that [Formula: see text] [Formula: see text] and let [Formula: see text] be generalized Hecke group associated to [Formula: see text] and [Formula: see text] Generalized Hecke group [Formula: see text] is generated by [Formula: see text] and [Formula: see text], where [Formula: see text] and [Formula: see text] In this paper, for positive integer [Formula: see text] we study the power subgroups [Formula: see text] of generalized Hecke groups [Formula: see text]. Also, we give some results about free normal subgroups of generalized Hecke groups [Formula: see text]

Normal Congruence Subgroups of Hecke Groups

2008 ◽  
Vol 15 (04) ◽  
pp. 707-720
Author(s):  
Bo Chen ◽  
Pingzhi Yuan
Keyword(s):  
Positive Integer ◽  
Dirichlet Series ◽  
Finite Index ◽  
Principal Congruence ◽  
Important Class ◽  
Congruence Subgroups ◽  
Discrete Subgroups ◽  
Hecke Groups ◽  
Hecke Group ◽  
Normal Congruence

Hecke groups are an important class of discrete subgroups of PSL(2, ℝ), which play an important role in the study of Dirichlet series. Subgroups with finite index of a Hecke group, which are called congruence subgroups, are often used. Let q be a positive integer with [Formula: see text]. For the Hecke group [Formula: see text], the structures of principal congruence subgroups and normal congruence subgroups of level m are investigated in many papers, where m is a prime or a power of an odd prime. In this paper, we deal with the case that the level m is a power of 2.

Normal Subgroups of Hecke Groups H(λ)

2009 ◽  
Vol 13 (2) ◽  
pp. 219-230 ◽  
Author(s):  
Özden Koruoğlu ◽  
Recep Sahin ◽  
Sebahattin İkikardes ◽  
Ismail Naci Cangül
Keyword(s):  
Normal Subgroups ◽  
Hecke Groups

GENERALIZED M*-GROUPS

2006 ◽  
Vol 16 (06) ◽  
pp. 1211-1219 ◽  
Author(s):  
RECEP SAHIN ◽  
SEBAHATTIN IKIKARDES ◽  
OZDEN KORUOGLU
Keyword(s):  
Positive Integer ◽  
Prime Number ◽  
Automorphism Groups ◽  
Klein Surface ◽  
Hecke Groups

A compact bordered Klein surface of algebraic genus p ≥ 2 has at most 12(p-1) automorphisms. Automorphism groups which attain this bound are called M*-groups. In this paper, firstly, we define generalized M*-groups. Then, we show that there is a relationship between the extended Hecke groups and generalized M*-groups. Finally, we prove that a generalized M*-groups G is supersoluble if and only if |G| = 4 · qr for q ≥ 3 prime number and for some positive integer r.

Classification of Normal Subgroups of Hecke Group H6 in Terms of Parabolic Class Number

2011 ◽  
Author(s):  
Aysun Yurttas ◽  
Musa Demirci ◽  
I. Naci Cangul ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Class Number ◽  
Normal Subgroups ◽  
Hecke Group

scholarly journals On Normal Subgroups of Generalized Hecke Groups

2016 ◽  
Vol 24 (2) ◽  
pp. 169-184
Author(s):  
Bilal Demir ◽  
Özden Koruoğlu ◽  
Recep Sahin
Keyword(s):  
Commutator Subgroup ◽  
Normal Subgroups ◽  
Hecke Groups

Abstract We consider the generalized Hecke groups Hp,q generated by X(z) = -(z -λp)-1, Y (z) = -(z +λq)-1 with and where 2 ≤ p ≤ q < ∞, p+q > 4. In this work we study the structure of genus 0 normal subgroups of generalized Hecke groups. We construct an interesting genus 0 subgroup called even subgroup, denoted by . We state the relation between commutator subgroup H′p,q of Hp,q defined in [1] and the even subgroup. Then we extend this result to extended generalized Hecke groups H̅p,q.

Upper Bounds for the Level of Normal Subgroups of Hecke Groups

2011 ◽  
Author(s):  
Musa Demirci ◽  
Aysun Yurttas ◽  
I. Naci Cangul ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
...  
Keyword(s):  
Upper Bounds ◽  
Normal Subgroups ◽  
Hecke Groups

scholarly journals Extension of partial endomorphisms of abelian groups

1963 ◽  
Vol 6 (1) ◽  
pp. 45-48 ◽  
Author(s):  
C. G. Chehata
Keyword(s):  
Abelian Group ◽  
Positive Integer ◽  
Abelian Groups ◽  
Normal Subgroups ◽  
Extension Group ◽  
Image Position ◽  
Necessary And Sufficient

It is known [1] that for a partial endomorphism μ of a group G that maps the subgroup A ⊆ G onto B ⊆ G. G to be extendable to a total endomorphism μ* of a supergroup G* ⊆ G such that μ an isomorphism on G*(μ*)m for some positive integer m, it is necessary and sufficient that there exist in G a sequence of normal subgroupssuch that L1 ƞA is the kernel of μ andfor ι = 1, 2,…, m–1.The question then arises whether these conditions could be simplified when the group G is abelian. In this paper it is shown not only that the conditions are simplified when Gis abelian but also that the extension group G*⊇G can be chosen as an abelian group.

Some character degree sets imply direct product

2016 ◽  
Vol 15 (10) ◽  
pp. 1650186
Author(s):  
Kamal Aziziheris ◽  
Heidar Sahrayi
Keyword(s):  
Finite Group ◽  
Positive Integer ◽  
Direct Product ◽  
Group Structure ◽  
Character Degree ◽  
Character Degrees ◽  
Normal Subgroups ◽  
Arbitrary Positive Integer ◽  
A Finite Group ◽  
Complex Characters

Let [Formula: see text] be the set of all irreducible complex characters of a finite group [Formula: see text]. In [K. Aziziheris, Determining group structure from sets of irreducible character degrees, J. Algebra 323 (2010) 1765–1782], we proved that if [Formula: see text] and [Formula: see text] are relatively prime integers greater than [Formula: see text], [Formula: see text] is prime not dividing [Formula: see text], and [Formula: see text] is a solvable group such that [Formula: see text], then under some conditions on [Formula: see text] and [Formula: see text], the group [Formula: see text] is the direct product of two normal subgroups, where [Formula: see text] and [Formula: see text]. In this paper, we replace [Formula: see text] by [Formula: see text], where [Formula: see text] is an arbitrary positive integer, and we obtain similar result. As an application, we show that if [Formula: see text] is a finite group with [Formula: see text] or [Formula: see text], then [Formula: see text] is a direct product of two non-abelian normal subgroups.

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