scholarly journals Suborbital graphs for a non-transitive action of the normalizer

Filomat ◽  
2019 ◽  
Vol 33 (2) ◽  
pp. 385-392 ◽  
Author(s):  
Murat Beşenk ◽  
Bahadır Güler ◽  
Abdurrahman Büyükkay
Keyword(s):  
Transitive Action ◽  
Suborbital Graphs ◽  
Suborbital Graph

In this paper, we investigate a suborbital graph for the normalizer of ?0(n) in PSL(2,R), where n will be of the form 32p2, p is a prime and p > 3. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.

scholarly journals Triangles in the suborbital graphs of the normalizer of $\Gamma_0(N)$

2020 ◽  
Vol 4 (2) ◽  
pp. 82
Author(s):  
Nazlı Yazıcı Gözütok ◽  
Bahadır Özgür Güler
Keyword(s):  
Prime Number ◽  
Transitive Action ◽  
Suborbital Graphs ◽  
Suborbital Graph

<p>In this paper, we investigate a suborbital graph for the normalizer of Γ<sub>0(<em>N</em>)</sub> ∈ PSL(2;<em>R</em>), where <em>N</em> will be of the form 2<sup>4</sup><em>p</em><sup>2</sup> such that <em>p</em> &gt; 3 is a prime number. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.</p>

scholarly journals Ranks, Subdegrees and Suborbital graphs of the product action of Affine Groups

2020 ◽  
Vol 19 ◽  
pp. 99-106
Author(s):  
Siahi Maxwell Agwanda ◽  
Patrick Kimani ◽  
Ireri Kamuti
Keyword(s):  
Direct Product ◽  
Cartesian Product ◽  
Galois Field ◽  
Suborbital Graphs ◽  
Affine Groups ◽  
Product Action ◽  
Definition Of ◽  
Suborbital Graph

The action of affine groups on Galois field has been studied.  For instance,  studied the action of on Galois field for  a power of prime.  In this paper, the rank and subdegree of the direct product of affine groups over Galois field acting on the cartesian product of Galois field is determined. The application of the definition of the product action is used to achieve this. The ranks and subdegrees are used in determination of suborbital graph, the non-trivial suborbital graphs that correspond to this action have been constructed using Sims procedure and were found to have a girth of 0, 3, 4 and 6.

ON SUBORBITAL GRAPHS FOR THE MODULAR GROUP

2001 ◽  
Vol 33 (6) ◽  
pp. 647-652 ◽  
Author(s):  
M. AKBAS
Keyword(s):  
Modular Group ◽  
Suborbital Graphs ◽  
Suborbital Graph

This paper proves a conjecture of G. A. Jones, D. Singerman and K. Wicks, that a suborbital graph for the modular group is a forest if and only if it contains no triangles.

scholarly journals On Suborbital Graphs for the Normalizer of $\Gamma_{0}(N)$

10.37236/205 ◽  
2009 ◽  
Vol 16 (1) ◽  
Author(s):  
Refik Keskin ◽  
Bahar Demirtürk
Keyword(s):  
Suborbital Graphs ◽  
Suborbital Graph

In this study, we deal with the conjecture given in [R. Keskin, Suborbital graph for the normalizer of $\Gamma _{0}(m)$, European Journal of Combinatorics 27 (2006) 193-206.], that when the normalizer of $\Gamma _{0}(N)$ acts transitively on ${\Bbb Q\cup\{\infty \}}$, any circuit in the suborbital graph $G(\infty,u/n)$ for the normalizer of $\Gamma _{0}(N),$ is of the form $$ v\rightarrow T(v)\rightarrow T^{2}(v)\rightarrow {\ \cdot \cdot \cdot } \rightarrow T^{k-1}(v)\rightarrow v, $$ where $n>1$, $v\in {\Bbb Q\cup \{\infty \}}$ and $T$ is an elliptic mapping of order $k$ in the normalizer of $\Gamma_{0}(N)$.

scholarly journals Affine cones over cubic surfaces are flexible in codimension one

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Alexander Perepechko
Keyword(s):  
Automorphism Group ◽  
Open Subset ◽  
Pezzo Surface ◽  
Ample Divisor ◽  
Transitive Action ◽  
Del Pezzo Surface ◽  
Codimension One ◽  
Cubic Surfaces ◽  
Special Automorphism ◽  
Del Pezzo

AbstractLet Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

scholarly journals Transitive action on finite points of a full shift and a finitary Ryan’s theorem

2017 ◽  
Vol 39 (06) ◽  
pp. 1637-1667 ◽  
Author(s):  
VILLE SALO
Keyword(s):  
Automorphism Group ◽  
Commutator Subgroup ◽  
Turing Machines ◽  
Finite Support ◽  
Transitive Action ◽  
Group Invariant ◽  
Finite Set ◽  
Transitivity Property ◽  
Full Shift ◽  
Subshifts Of Finite Type

We show that on the four-symbol full shift, there is a finitely generated subgroup of the automorphism group whose action is (set-theoretically) transitive of all orders on the points of finite support, up to the necessary caveats due to shift-commutation. As a corollary, we obtain that there is a finite set of automorphisms whose centralizer is $\mathbb{Z}$ (the shift group), giving a finitary version of Ryan’s theorem (on the four-symbol full shift), suggesting an automorphism group invariant for mixing subshifts of finite type (SFTs). We show that any such set of automorphisms must generate an infinite group, and also show that there is also a group with this transitivity property that is a subgroup of the commutator subgroup and whose elements can be written as compositions of involutions. We ask many related questions and prove some easy transitivity results for the group of reversible Turing machines, topological full groups and Thompson’s  $V$ .

scholarly journals Invariant connections and invariant holomorphic bundles on homogeneous manifolds

2014 ◽  
Vol 12 (1) ◽  
pp. 1-13
Author(s):  
Indranil Biswas ◽  
Andrei Teleman
Keyword(s):  
Lie Group ◽  
Complex Structure ◽  
Differentiable Manifold ◽  
Equivalence Classes ◽  
Transitive Action ◽  
Isomorphism Classes ◽  
Finite Dimensional ◽  
Group A ◽  
Holomorphic Bundles ◽  
Invariant Gauge

AbstractLet X be a differentiable manifold endowed with a transitive action α: A×X→X of a Lie group A. Let K be a Lie group. Under suitable technical assumptions, we give explicit classification theorems, in terms of explicit finite dimensional quotients, of three classes of objects:equivalence classes of α-invariant K-connections on X α-invariant gauge classes of K-connections on X, andα-invariant isomorphism classes of pairs (Q,P) consisting of a holomorphic Kℂ-bundle Q → X and a K-reduction P of Q (when X has an α-invariant complex structure).

scholarly journals Solutions to some congruence equations via suborbital graphs

SpringerPlus ◽  
2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Bahadır Özgür Güler ◽  
Tuncay Kör ◽  
Zeynep Şanlı
Keyword(s):  
Suborbital Graphs

scholarly journals On congruence equations arising from suborbital graphs

2019 ◽  
Vol 43 (5) ◽  
pp. 2396-2404 ◽  
Author(s):  
Bahadır Özgür GÜLER ◽  
Murat BEŞENK ◽  
Serkan KADER
Keyword(s):  
Suborbital Graphs

scholarly journals Amalgams Determined By Locally Projective Actions

2004 ◽  
Vol 176 ◽  
pp. 19-98 ◽  
Author(s):  
A. A. Ivanov ◽  
S. V. Shpectorov
Keyword(s):  
Linear Group ◽  
Infinite Series ◽  
Connected Graph ◽  
Interesting Case ◽  
Simple Groups ◽  
Transitive Action ◽  
Sporadic Simple Groups ◽  
Global Stabilizer

AbstractA locally projective amalgam is formed by the stabilizer G(x) of a vertex x and the global stabilizer G{x, y} of an edge (containing x) in a group G, acting faithfully and locally finitely on a connected graph Γ of valency 2n - 1 so that (i) the action is 2-arc-transitive; (ii) the subconstituent G(x)Γ(x) is the linear group SLn(2) = Ln(2) in its natural doubly transitive action and (iii) [t, G{x, y}] < O2(G(x) n G{x, y}) for some t G G{x, y} \ G(x). D. Z. Djokovic and G. L. Miller [DM80], used the classical Tutte’s theorem [Tu47], to show that there are seven locally projective amalgams for n = 2. Here we use the most difficult and interesting case of Trofimov’s theorem [Tr01] to extend the classification to the case n > 3. We show that besides two infinite series of locally projective amalgams (embedded into the groups AGLn(2) and O2n+(2)) there are exactly twelve exceptional ones. Some of the exceptional amalgams are embedded into sporadic simple groups M22, M23, Co2, J4 and BM. For each of the exceptional amalgam n = 3, 4 or 5.

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