scholarly journals p-Groups of automorphisms of compact non-orientable Riemann surfaces

2021 ◽  
Vol 115 (4) ◽  
Author(s):  
E. Bujalance ◽  
F. J. Cirre ◽  
J. M. Gamboa
Keyword(s):  
Automorphism Group ◽  
Riemann Surfaces ◽  
Upper Bounds ◽  
Full Automorphism Group ◽  
Number Of Generators ◽  
Groups Of Automorphisms ◽  
Topological Genus

AbstractWe study p-groups of automorphisms of compact non-orientable Riemann surfaces of topological genus $$g\ge 3$$ g ≥ 3 . We obtain upper bounds of the order of such groups in terms of p,  g and the minimal number of generators of the group. We also determine those values of g for which these bounds are sharp. Furthermore, the same kind of results are obtained when the p-group acts as the full automorphism group of the surface.

scholarly journals Automorphisms of compact non-orientable Riemann surfaces

1971 ◽  
Vol 12 (1) ◽  
pp. 50-59 ◽  
Author(s):  
D. Singerman
Keyword(s):  
Riemann Surface ◽  
Automorphism Group ◽  
Riemann Surfaces ◽  
Group Of Automorphisms ◽  
Groups Of Automorphisms ◽  
Definition Of ◽  
Orientable Surfaces

Using the definition of a Riemann surface, as given for example by Ahlfors and Sario, one can prove that all Riemann surfaces are orientable. However by modifying their definition one can obtain structures on non-orientable surfaces. In fact nonorientable Riemann surfaces have been considered by Klein and Teichmüller amongst others. The problem we consider here is to look for the largest possible groups of automorphisms of compact non-orientable Riemann surfaces and we find that this throws light on the corresponding problem for orientable Riemann surfaces, which was first considered by Hurwitz [1]. He showed that the order of a group of automorphisms of a compact orientable Riemann surface of genus g cannot be bigger than 84(g – 1). This bound he knew to be attained because Klein had exhibited a surface of genus 3 which admitted PSL (2, 7) as its automorphism group, and the order of PSL(2, 7) is 168 = 84(3–1). More recently Macbeath [5, 3] and Lehner and Newman [2] have found infinite families of compact orientable surfaces for which the Hurwitz bound is attained, and in this paper we shall exhibit some new families.

Complete set of Genera of Compact Riemann Surfaces with reference to the point Group of Sulphur (S8) Molecule

2020 ◽  
Vol 32 (7) ◽  
pp. 88-92
Author(s):  
RAFIQUL ISLAM ◽  
◽  
CHANDRA CHUTIA ◽  
Keyword(s):  
Automorphism Group ◽  
Riemann Surfaces ◽  
Point Group ◽  
Finite Point ◽  
Group Of Automorphisms ◽  
Complete Set ◽  
Compact Riemann Surfaces ◽  
Group Of Symmetries

In this paper we consider the group of symmetries of the Sulphur molecule (S8 ) which is a finite point group of order 16 denote by D16 generated by two elements having the presentation { u\upsilon/u2= \upsilon8 = (u\upsilon)2 = 1} and find the complete set of genera (g ≥ 2) of Compact Riemann surfaces on which D16 acts as a group of automorphisms as follows: D16 the group of symmetries of the sulphur (S8) molecule of order 16 acts as an automorphism group of a compact Riemann surfaces of genus g ≥ 2 if and only if there are integers \lambda and \mu such that \lambda \leq 1 and \mu \geq 1 and g=\lambda +8\mu (\geq2) , \mu\geq |\lambda|

scholarly journals Cohomological finiteness conditions and centralisers in generalisations of Thompson’s group V

2016 ◽  
Vol 28 (5) ◽  
pp. 909-921 ◽  
Author(s):  
Conchita Martínez-Pérez ◽  
Francesco Matucci ◽  
Brita E. A. Nucinkis
Keyword(s):  
Automorphism Group ◽  
Finiteness Conditions ◽  
Group V ◽  
Full Automorphism Group ◽  
Finite Subgroups ◽  
Thompson’S Group

AbstractWe consider generalisations of Thompson’s group V, denoted by ${V_{r}(\Sigma)}$, which also include the groups of Higman, Stein and Brin. We show that, under some mild hypotheses, ${V_{r}(\Sigma)}$ is the full automorphism group of a Cantor algebra. Under some further minor restrictions, we prove that these groups are of type ${\operatorname{F}_{\infty}}$ and that this implies that also centralisers of finite subgroups are of type ${\operatorname{F}_{\infty}}$.

scholarly journals Pentavalent arc-transitive Cayley graphs on Frobenius groups with soluble vertex stabilizer

2019 ◽  
Vol 17 (1) ◽  
pp. 513-518
Author(s):  
Hailin Liu
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Cayley Graphs ◽  
Frobenius Groups ◽  
Full Automorphism Group

Abstract A Cayley graph Γ is said to be arc-transitive if its full automorphism group AutΓ is transitive on the arc set of Γ. In this paper we give a characterization of pentavalent arc-transitive Cayley graphs on a class of Frobenius groups with soluble vertex stabilizer.

scholarly journals Rooted trees, strong cofinality and ample generics

2012 ◽  
Vol 154 (2) ◽  
pp. 213-223
Author(s):  
MACIEJ MALICKI
Keyword(s):  
Automorphism Group ◽  
Open Subgroup ◽  
Rooted Trees ◽  
Full Automorphism Group

AbstractWe characterize those countable rooted trees with non-trivial components whose full automorphism group has uncountable strong cofinality, and those whose full automorphism group contains an open subgroup with ample generics.

A 2-ARC TRANSITIVE PENTAVALENT CAYLEY GRAPH OF 

2016 ◽  
Vol 93 (3) ◽  
pp. 441-446 ◽  
Author(s):  
BO LING ◽  
BEN GONG LOU
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Cayley Graphs ◽  
Discrete Math ◽  
Simple Groups ◽  
Alternating Group ◽  
Full Automorphism Group ◽  
Symmetric Graphs

Zhou and Feng [‘On symmetric graphs of valency five’, Discrete Math. 310 (2010), 1725–1732] proved that all connected pentavalent 1-transitive Cayley graphs of finite nonabelian simple groups are normal. We construct an example of a nonnormal 2-arc transitive pentavalent symmetric Cayley graph on the alternating group $\text{A}_{39}$. Furthermore, we show that the full automorphism group of this graph is isomorphic to the alternating group $\text{A}_{40}$.

scholarly journals QUASI-RANDOM PROFINITE GROUPS

2014 ◽  
Vol 57 (1) ◽  
pp. 181-200
Author(s):  
MOHAMMAD BARDESTANI ◽  
KEIVAN MALLAHI-KARAI
Keyword(s):  
Functional Analysis ◽  
Automorphism Group ◽  
Measurable Subset ◽  
Upper Bounds ◽  
Minimal Degree ◽  
Profinite Groups ◽  
Lower And Upper Bounds ◽  
Seminal Paper ◽  
Regular Tree ◽  
Special Subgroup

AbstractInspired by Gowers' seminal paper (W. T. Gowers, Comb. Probab. Comput.17(3) (2008), 363–387, we will investigate quasi-randomness for profinite groups. We will obtain bounds for the minimal degree of non-trivial representations of SLk(ℤ/(pnℤ)) and Sp2k(ℤ/(pnℤ)). Our method also delivers a lower bound for the minimal degree of a faithful representation of these groups. Using the suitable machinery from functional analysis, we establish exponential lower and upper bounds for the supremal measure of a product-free measurable subset of the profinite groups SLk(ℤp) and Sp2k(ℤp). We also obtain analogous bounds for a special subgroup of the automorphism group of a regular tree.

Full automorphism group of the generalized symplectic graph

2013 ◽  
Vol 56 (7) ◽  
pp. 1509-1520 ◽  
Author(s):  
LiWei Zeng ◽  
Zhao Chai ◽  
RongQuan Feng ◽  
ChangLi Ma
Keyword(s):  
Automorphism Group ◽  
Full Automorphism Group

Automorphism groups of trivial strongly minimal structures

2003 ◽  
Vol 68 (2) ◽  
pp. 644-668
Author(s):  
Thomas Blossier
Keyword(s):  
Automorphism Group ◽  
Automorphism Groups ◽  
Profinite Group ◽  
Hnn Extensions ◽  
Minimal Structure ◽  
Groups Of Automorphisms ◽  
Stabilizer Of A Point

AbstractWe study automorphism groups of trivial strongly minimal structures. First we give a characterization of structures of bounded valency through their groups of automorphisms. Then we characterize the triplets of groups which can be realized as the automorphism group of a non algebraic component, the subgroup stabilizer of a point and the subgroup of strong automorphisms in a trivial strongly minimal structure, and also we give a reconstruction result. Finally, using HNN extensions we show that any profinite group can be realized as the stabilizer of a point in a strongly minimal structure of bounded valency.

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