Priv.-Doz. Dr. Hubert Kiechle

@article{434bf391b5e24fe99a9abf2e5961e485,

title = "Overlaps in field generated circular planar nearrings",

abstract = "Abs tract. We investigate circular planar nearrings con-structed from {\H o}nite {\H o}elds as well the complex number {\H o}eld using a multiplicative subgroup of order k, and characterize the overlaps of the basic graphs which arise in the associated 2-designs.",

keywords = "2-design, circularity, Ferrero pair, overlap",

author = "Ke, {Wen Fong} and Hubert Kiechle",

note = "Publisher Copyright: {\textcopyright} Algebra and Discrete Mathematics.",

year = "2023",

doi = "10.12958/adm2130",

language = "English",

volume = "35",

pages = "134--167",

journal = "Algebra and Discrete Mathematics",

issn = "1726-3255",

publisher = "Institute of Applied Mathematics And Mechanics of the National Academy of Sciences of Ukraine",

number = "2",

@article{a71dff905f46418e8898e13ca523799f,

title = "Planar nearrings on the Euclidean plane",

abstract = "Planar near-rings are generalized rings which can serve as coordinate domains for geometric structures in which each pair of nonparallel lines has a unique point of intersection. It is known that all planar nearrings can be constructed from regular groups of automorphisms of groups which can be viewed as the “action groups” of the planar nearring. In this article, we study planar nearrings whose additive group is (R n ,+) , in particular, n = 1 and 2. It is natural to study topological planar nearrings in this context, following ideas of the late Kenneth D. Magill, Jr. In the case of n = 1, we characterize all topological planar nearrings by their action groups (R ∗ ,⋅) or (R + ,⋅) . For n = 2, these action groups and the circle group (U,⋅) seem to be the most interesting cases, but the last case can be excluded completely. As a consequence, we obtain characterizations of the semi-homogeneous continuous mappings from R n to R for n = 1 and 2. Such a mapping f enjoys the property that f(f(u)v) = f(u)f(v) for all u,v∈R n . When f(R n )=R + , f is a positive homogeneous mapping of degree 1.",

keywords = "Primary 16Y30, Secondary 16W80",

author = "Wen-Fong Ke and Hubert Kiechle and G{\"u}nter Pilz and Gerhard Wendt",

year = "2014",

doi = "10.1007/s00022-014-0221-7",

language = "English",

volume = "105",

pages = "577--599",

journal = "Journal of Geometry",

issn = "0047-2468",

publisher = "Birkhauser Verlag Basel",

number = "3",

@article{91656bd42be643cd85348badad34165e,

title = "Automorphisms of certain design groups II",

abstract = "Let Φ be a group acting semiregularly as automorphisms on the group (N, +). This gives rise to a certain 2-design (N, BΦ). The group structure of N is compatible with the geometric structure of this 2-design, and we call (N, BΦ, +) a design group. Extending our previous results, we study the question of when such design groups are isomorphic. Let Ψ be another group acting on N so that (N, BΨ, +) is also a design group. Suppose further that for k = | Φ | we have | N / [N, N] | > 2 k2 - 6 k + 1. We show that (N, BΦ, +) and (N, BΨ, +) are isomorphic if and only if Φ and Ψ are conjugate in the automorphism group of N.",

keywords = "Design group, Ferrero pair, Semiregular automorphisms",

author = "Beidar, {Kostia I.} and Ke, {Wen Fong} and Hubert Kiechle",

year = "2007",

month = jul,

day = "15",

doi = "10.1016/j.jalgebra.2006.11.026",

language = "English",

volume = "313",

pages = "672--686",

journal = "Journal of algebra",

issn = "0021-8693",

publisher = "Academic Press Inc.",

number = "2",

@article{b565d35d3c1440fd85f512882266a30a,

title = "Circularity of finite groups without fixed points",

abstract = "Let Φ be a fixed point free group given by the presentation « A, B\,\vert\, A^\mu=1,\, B^\nu=A^t,\, BAB-1=Aρ» where μ and ρ are relative prime numbers, t = μ/s and s = gcd(ρ - 1,μ), and ν is the order of ρ modulo μ. We prove that if (1) ν = 2, and (2) Φ is embeddable into the multiplicative group of some skew field, then Φ is circular. This means that there is some additive group N on which Φ acts fixed point freely, and |(Φ(a)+b)≠(Φ(c)+d)| ≤ 2 whenever a,b,c,d N, a ≠ 0 ≠ c, are such that Φ(a)+b ≠ Φ(c)+d.",

keywords = "Circular, Ferrero pair, Metacyclic group, Skewfield",

author = "Beidar, {Kostia I.} and Ke, {Wen Fong} and Hubert Kiechle",

year = "2005",

month = apr,

doi = "10.1007/s00605-004-0268-x",

language = "English",

volume = "144",

pages = "265--273",

journal = "Monatshefte fur Mathematik",

issn = "0026-9255",

publisher = "Springer-Verlag Wien",

number = "4",

@article{87554cfd91594752b9ea5363f1b553ad,

title = "Infinite simple Bol loops",

abstract = "If the left multiplication group of a loop is simple, then the loop is simple. We use this observation to give examples of infinite simple Bol loops.",

keywords = "Bol loop, Bruck loop, K-loop",

author = "Hubert Kiechle and Kinyon, {Michael K.}",

note = "Publisher Copyright: {\textcopyright} 2004 Charles University, Faculty of Mathematics and Physics.",

year = "2004",

language = "English",

volume = "45",

pages = "275--278",

journal = "Commentationes Mathematicae Universitatis Carolinae",

issn = "0010-2628",

publisher = "Charles University, Faculty of Mathematics and Physics",

number = "2",

@article{d10606563b5b4404a586e8223a3d2649,

title = "Frobenius groups with many involutions",

abstract = "We consider a special class of Frobenius Groups, which generalizes the class of sharply 2-transitive groups in such a way that the construction of a neardomain can be generalized to the construction of a K-loop. The group then is shown to be a quasidirect product of that K-loop by a suitable automorphism group. The major advantage of this point of view is the existence of examples which are hoped to shed some light on the still open problem of the existence of proper neardomains.",

author = "Hubert Kiechle",

year = "2002",

month = aug,

day = "28",

doi = "10.1016/S0012-365X(01)00401-0",

language = "English",

volume = "255",

pages = "235--247",

journal = "Discrete mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "1-3",

@article{0f40595c7ad647dbb9b0cf86b7190334,

title = "On the extension of involutorial Bol loops",

abstract = "The group theoretical problem of the existence of a system of representatives T of the subgroup H of G such that T consists of conjugacy classes of involutions leads to the theory of Bol loops of exponent 2. In this paper, we develop a theory of extensions of such loops and give two applications of the theory. First, we classify all (left) Bol loops of exponent 2 of order 16; second, we classify all Bol loops of exponent 2 whose right nucleus has index 2. In particular, we give a class of examples of non-nilpotent such Bol loops.",

author = "Hubert Kiechle and Nagy, {G{\'a}bor P.}",

year = "2002",

doi = "10.1007/BF02941674",

language = "English",

volume = "72",

pages = "235--250",

journal = "Abhandlungen aus dem Mathematischen Seminar der Universitat Hamburg",

issn = "0025-5858",

publisher = "Springer",