scholarly journals Characterization of the Hilbert ball by its automorphism group

2002 ◽  
Vol 354 (7) ◽  
pp. 2797-2818 ◽  
Author(s):  
Kang-Tae Kim ◽  
Steven G. Krantz
Keyword(s):  
Automorphism Group ◽  
Hilbert Ball

scholarly journals HEYDE’S CHARACTERIZATION THEOREM FOR DISCRETE ABELIAN GROUPS

2010 ◽  
Vol 88 (1) ◽  
pp. 93-102 ◽  
Author(s):  
MARGARYTA MYRONYUK
Keyword(s):  
Abelian Group ◽  
Automorphism Group ◽  
Real Line ◽  
Linear Form ◽  
Conditional Distribution ◽  
Random Variables ◽  
Characterization Theorem ◽  
Gaussian Distributions ◽  
Discrete Abelian Group

AbstractLet X be a countable discrete abelian group with automorphism group Aut(X). Let ξ1 and ξ2 be independent X-valued random variables with distributions μ1 and μ2, respectively. Suppose that α1,α2,β1,β2∈Aut(X) and β1α−11±β2α−12∈Aut(X). Assuming that the conditional distribution of the linear form L2 given L1 is symmetric, where L2=β1ξ1+β2ξ2 and L1=α1ξ1+α2ξ2, we describe all possibilities for the μj. This is a group-theoretic analogue of Heyde’s characterization of Gaussian distributions on the real line.

Kleinian characterization of asymptotic symmetries of real general relativity

1993 ◽  
Vol 441 (1913) ◽  
pp. 465-471 ◽  
Keyword(s):  
General Relativity ◽  
Automorphism Group ◽  
Group Action ◽  
Radon Transform ◽  
Symmetry Groups ◽  
Asymptotic Symmetry ◽  
The Real ◽  
The Given ◽  
Asymptotic Symmetries

According to Klein’s Erlanger programme, one may (indirectly) specify a geometry by giving a group action. Conversely, given a group action, one may ask for the corresponding geometry. Recently, I showed that the real asymptotic symmetry groups of general relativity (in any signature) have natural ‘projective’ classical actions on suitable ‘Radon transform’ spaces of affine 3-planes in flat 4-space. In this paper, I give concrete models for these groups and actions. Also, for the ‘atomic’ cases, I give geometric structures for the spaces of affine 3-planes for which the given actions are the automorphism group.

scholarly journals Cubic arc-transitive Cayley graphs on Frobenius groups

2018 ◽  
Vol 17 (07) ◽  
pp. 1850126 ◽  
Author(s):  
Hailin Liu ◽  
Lei Wang
Keyword(s):  
Automorphism Group ◽  
Cayley Graph ◽  
Cayley Graphs ◽  
Frobenius Groups

A Cayley graph [Formula: see text] is called arc-transitive if its automorphism group [Formula: see text] is transitive on the set of arcs in [Formula: see text]. In this paper, we give a characterization of cubic arc-transitive Cayley graphs on a class of Frobenius groups.

scholarly journals Automorphisms of Regular Wreath Product -Groups

2009 ◽  
Vol 2009 ◽  
pp. 1-12 ◽  
Author(s):  
Jeffrey M. Riedl
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Representation Theory ◽  
Wreath Product ◽  
Cyclic Group ◽  
Product Group ◽  
Finite Cyclic Group ◽  
Arbitrary Finite Group

We present a useful new characterization of the automorphisms of the regular wreath product group of a finite cyclic -group by a finite cyclic -group, for any prime , and we discuss an application. We also present a short new proof, based on representation theory, for determining the order of the automorphism group Aut(), where is the regular wreath product of a finite cyclic -group by an arbitrary finite -group.

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.

Quasirecognition of E6(q) by the orders of maximal abelian subgroups

2018 ◽  
Vol 17 (07) ◽  
pp. 1850122 ◽  
Author(s):  
Zahra Momen ◽  
Behrooz Khosravi
Keyword(s):  
Finite Group ◽  
Automorphism Group ◽  
Simple Group ◽  
Outer Automorphism ◽  
Composition Factor ◽  
Outer Automorphism Group ◽  
Abelian Subgroups ◽  
A Finite Group ◽  
Nonabelian Composition Factor

In [Li and Chen, A new characterization of the simple group [Formula: see text], Sib. Math. J. 53(2) (2012) 213–247.], it is proved that the simple group [Formula: see text] is uniquely determined by the set of orders of its maximal abelian subgroups. Also in [Momen and Khosravi, Groups with the same orders of maximal abelian subgroups as [Formula: see text], Monatsh. Math. 174 (2013) 285–303], the authors proved that if [Formula: see text], where [Formula: see text] is not a Mersenne prime, then every finite group with the same orders of maximal abelian subgroups as [Formula: see text], is isomorphic to [Formula: see text] or an extension of [Formula: see text] by a subgroup of the outer automorphism group of [Formula: see text]. In this paper, we prove that if [Formula: see text] is a finite group with the same orders of maximal abelian subgroups as [Formula: see text], then [Formula: see text] has a unique nonabelian composition factor which is isomorphic to [Formula: see text].

scholarly journals On generalized quaternion algebras

1980 ◽  
Vol 3 (2) ◽  
pp. 237-245 ◽  
Author(s):  
George Szeto
Keyword(s):  
Automorphism Group ◽  
Commutative Ring ◽  
Galois Extension ◽  
Ring Extension ◽  
Separable Extension ◽  
Quaternion Algebras ◽  
Generalized Quaternion

LetBbe a commutative ring with1, andG(={σ})an automorphism group ofBof order2. The generalized quaternion ring extensionB[j]overBis defined byS. Parimala andR. Sridharan such that (1)B[j]is a freeB-module with a basis{1,j}, and (2)j2=−1andjb=σ(b)jfor eachbinB. The purpose of this paper is to study the separability ofB[j]. The separable extension ofB[j]overBis characterized in terms of the trace(=1+σ)ofBover the subring of fixed elements underσ. Also, the characterization of a Galois extension of a commutative ring given by Parimala and Sridharan is improved.

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.

scholarly journals On characterizations of a center Galois extension

2000 ◽  
Vol 23 (11) ◽  
pp. 753-758 ◽  
Author(s):  
George Szeto ◽  
Lianyong Xue
Keyword(s):  
Automorphism Group ◽  
Galois Group ◽  
Galois Extension ◽  
The Ideal

LetBbe a ring with1,  Cthe center ofB,  Ga finite automorphism group ofB, andBGthe set of elements inBfixed under each element inG. Then, it is shown thatBis a center Galois extension ofBG(that is,Cis a Galois algebra overCGwith Galois groupG|C≅G) if and only if the ideal ofBgenerated by{c−g(c)|c∈C}isBfor eachg≠1inG. This generalizes the well known characterization of a commutative Galois extensionCthatCis a Galois extension ofCGwith Galois groupGif and only if the ideal generated by{c−g(c)|c∈C}isCfor eachg≠1inG. Some more characterizations of a center Galois extensionBare also given.

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