The full group of automorphisms of non-orientable unbordered Klein surfaces of topological genus 7

2017 ◽  
Vol 31 (1) ◽  
pp. 247-261
Author(s):  
Adrián Bacelo
Keyword(s):  
Full Group ◽  
Klein Surfaces ◽  
Group Of Automorphisms ◽  
Topological Genus

scholarly journals ON THE CONNECTEDNESS OF THE BRANCH LOCI OF NON-ORIENTABLE UNBORDERED KLEIN SURFACES OF LOW GENUS

2014 ◽  
Vol 57 (1) ◽  
pp. 211-230 ◽  
Author(s):  
E. BUJALANCE ◽  
J. J. ETAYO ◽  
E. MARTÍNEZ ◽  
B. SZEPIETOWSKI
Keyword(s):  
Moduli Space ◽  
Prime Order ◽  
Topological Conjugacy ◽  
Branch Locus ◽  
Klein Surfaces ◽  
Topological Genus

AbstractThis paper is devoted to determine the connectedness of the branch loci of the moduli space of non-orientable unbordered Klein surfaces. We obtain a result similar to Nielsen's in order to determine topological conjugacy of automorphisms of prime order on such surfaces. Using this result we prove that the branch locus is connected for surfaces of topological genus 4 and 5.

Small Directed Strongly Regular Graphs

2020 ◽  
Vol 27 (01) ◽  
pp. 11-30
Author(s):  
Štefan Gyürki
Keyword(s):  
Strongly Regular Graphs ◽  
Regular Graphs ◽  
Full Group ◽  
Group Of Automorphisms ◽  
Strongly Regular ◽  
Directed Strongly Regular Graphs

The goal of the present paper is to provide a gallery of small directed strongly regular graphs. For each graph of order n ≤ 12 and valency k < n/2, a diagram is depicted, its relation to other small directed strongly regular graphs is revealed, the full group of automorphisms is described, and some other nice properties are given. To each graph a list of interesting subgraphs is provided as well.

scholarly journals Outer automorphisms of hypercentral p-groups

1995 ◽  
Vol 37 (2) ◽  
pp. 243-247
Author(s):  
Orazio Puglisi
Keyword(s):  
Nilpotent Group ◽  
Full Group ◽  
Finite Nilpotent Group ◽  
Group Of Automorphisms ◽  
Outer Automorphisms ◽  
Inner Automorphisms

In his celebrated paper [3] Gaschiitz proved that any finite non-cyclic p-group always admits non-inner automorphisms of order a power of p. In particular this implies that, if G is a finite nilpotent group of order bigger than 2, then Out (G) = Aut(G)/Inn(G) =≠1. Here, as usual, we denote by Aut (G) the full group of automorphisms of G while Inn (G) stands for the group of inner automorphisms, that is automorphisms induced by conjugation by elements of G. After Gaschiitz proved this result, the following question was raised: “if G is an infinite nilpotent group, is it always true that Out (G)≠1?”

scholarly journals Minimum topological genus of compact bordered Klein surfaces admitting a prime-power automorphism

1995 ◽  
Vol 37 (2) ◽  
pp. 221-232 ◽  
Author(s):  
E. Bujalance ◽  
J. M. Gamboa ◽  
C. Maclachlan
Keyword(s):  
Finite Group ◽  
Riemann Surface ◽  
Riemann Surfaces ◽  
Prime Power ◽  
Compact Riemann Surface ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Abelian Case ◽  
Power Automorphism ◽  
Topological Genus

In the nineteenth century, Hurwitz [8] and Wiman [14] obtained bounds for the order of the automorphism group and the order of each automorphism of an orientable and unbordered compact Klein surface (i. e., a compact Riemann surface) of topological genus g s 2. The corresponding results of bordered surfaces are due to May, [11], [12]. These may be considered as particular cases of the general problem of finding the minimum topological genus of a surface for which a given finite group G is a group of automorphisms. This problem was solved for cyclic and abelian G by Harvey [7] and Maclachlan [10], respectively, in the case of Riemann surfaces and by Bujalance [2], Hall [6] and Gromadzki [5] in the case of non-orientable and unbordered Klein surfaces. In dealing with bordered Klein surfaces, the algebraic genus—i. e., the topological genus of the canonical double covering, (see Alling-Greenleaf [1])—was minimized by Bujalance- Etayo-Gamboa-Martens [3] in the case where G is cyclic and by McCullough [13] in the abelian case.

scholarly journals Arithmetic E8 Lattices with Maximal Galois Action

2009 ◽  
Vol 12 ◽  
pp. 144-165 ◽  
Author(s):  
Anthony Várilly-Alvarado ◽  
David Zywina
Keyword(s):  
Elliptic Curves ◽  
Weyl Group ◽  
Number Fields ◽  
Picard Group ◽  
Del Pezzo Surfaces ◽  
Full Group ◽  
Group Of Automorphisms ◽  
Intersection Pairing ◽  
Galois Action ◽  
Del Pezzo

AbstractWe construct explicit examples of E8 lattices occurring in arithmetic for which the natural Galois action is equal to the full group of automorphisms of the lattice, i.e., the Weyl group of E8. In particular, we give explicit elliptic curves over Q(t) whose Mordell-Weil lattices are isomorphic to E8 and have maximal Galois action.Our main objects of study are del Pezzo surfaces of degree 1 over number fields. The geometric Picard group, considered as a lattice via the negative of the intersection pairing, contains a sublattice isomorphic to E8. We construct examples of such surfaces for which the action of Galois on the geometric Picard group is maximal.

scholarly journals Orientable and non-orientable Klein surfaces with maximal symmetry

1985 ◽  
Vol 26 (1) ◽  
pp. 31-34 ◽  
Author(s):  
David Singerman
Keyword(s):  
Finite Group ◽  
Upper Bound ◽  
Closed Surface ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Maximal Symmetry ◽  
Group Of Automorphisms ◽  
G 12 ◽  
Image Position ◽  
A Finite Group

Let X be a bordered Klein surface, by which we mean a Klein surface with non-empty boundary. X is characterized topologically by its orientability, the number k of its boundary components and the genus p of the closed surface obtained by filling in all the holes. The algebraic genus g of X is defined by.If g≥2 it is known that if G is a group of automorphisms of X then |G|≤12(g-l) and that the upper bound is attained for infinitely many values of g ([4], [5]). A bordered Klein surface for which this upper bound is attained is said to have maximal symmetry. A group of 12(g-l) automorphisms of a bordered Klein surface of algebraic genus g is called an M*-group and it is known that a finite group G is an M*-group if and only if it is generated by 3 non-trivial elements T1, T2, T3 which obey the relations([4]).

scholarly journals Automorphism groups of complex doubles of Klein surfaces

1994 ◽  
Vol 36 (3) ◽  
pp. 313-330 ◽  
Author(s):  
E. Bujalance ◽  
A. F. Costa ◽  
G. Gromadzki ◽  
D. Singerman
Keyword(s):  
Riemann Surface ◽  
Compact Riemann Surface ◽  
Automorphism Groups ◽  
Natural Question ◽  
Klein Surface ◽  
Klein Surfaces ◽  
Maximal Symmetry ◽  
Group Of Automorphisms

In this paper we consider complex doubles of compact Klein surfaces that have large automorphism groups. It is known that a bordered Klein surface of algebraic genus g > 2 has at most 12(g − 1) automorphisms. Surfaces for which this bound is sharp are said to have maximal symmetry. The complex double of such a surface X is a compact Riemann surface X+ of genus g and it is easy to see that if G is the group of automorphisms of X then C2 × G is a group of automorphisms of X+. A natural question is whether X+ can have a group that strictly contains C2 × G. In [8] C. L. May claimed the following interesting result: there is a unique Klein surface X with maximal symmetry for which Aut X+ properly contains C2 × Aut X (where Aut X+ denotes the group of conformal and anticonformal automorphisms of X+).

Admissible subgroups of full ergodic groups

1996 ◽  
Vol 16 (6) ◽  
pp. 1221-1239
Author(s):  
Andrey Fedorov ◽  
Ben-Zion Rubshtein
Keyword(s):  
Finite Group ◽  
Lebesgue Space ◽  
Complete Solution ◽  
Countable Group ◽  
Type Ii ◽  
Full Group ◽  
Group Of Automorphisms ◽  
Countable Subgroup

AbstractLet G be a countable group of automorphisms of a Lebesgue space (X, m) and let [G] be the full group of G. For a pair of countable ergodic subgroups H1 and H2 of [G], the following problem is considered: when are the full subgroups [H1] and [H2] conjugate in the normalizer N[G] = {g ∈ Aut X: g[G]g-1 = [G]} of [G]. A complete solution of the problem is given in the case when [G] is an approximately finite group of type II and [H] is admissible, in the sense that there exists an ergodic subgroup [H0] of [G] and a countable subgroup Γ ⊂ N[H0] consisting of automorphisms which are outer for [H0], such that [H0] ⊂ [G] and the full subgroup [Ho, Γ] generated by [H0] and Γ coincides with [G].

Sign in / Sign up

Export Citation Format

Share Document