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1.
Helmut Mäurer 《Journal of Geometry》2007,86(1-2):150-153
An involutory automorphism of an inversive plane whose set of fixed points consists of exactly two points resp. of a circle
is called a harmonic involution resp. an inversion. In this paper we study inversive planes with sufficiently many such involutions.
Herrn Walter Benz zum 75. Geburtstag gewidmet 相似文献
2.
J. A. Thas 《Inventiones Mathematicae》1994,118(1):133-139
Summary LetJ be a finite inversive plane of odd orderq. If for at least one pointp ofJ the internal affine planeJ
p
is Desarguesian, thenJ is Miquelian. Other formulation: the finite Desarguesian affine plane of odd orderq has a unique one point extension; this extension is the Miquelian inversive plane of orderq. It follows that there is a unique inversive plane of orderq, withq{3, 5, 7}.Oblatum 23-X-1992 & 24-I-1994 相似文献
3.
4.
Chat Yin Ho 《Geometriae Dedicata》1995,55(1):59-70
A planar Singer group is a collineation group of a finite (in this article) projective plane acting regularly on the points of the plane. Theorem 1 gives a characterization of abelian planar Singer groups. This leads to a necessary and sufficient condition for an inner automorphism to be a multiplier. The Sylow 2-structure of a multiplier group and some of its consequences are given in Theorem 3. One important result in studying multipliers of an abelian Singer group is the existence of a common fixed line. We extend this to an arbitrary planar Singer group in Theorem 4. Theorem 5 studies the order of an abelian group of multiplers. If this order equals to the order of the plane plus 1, then the number of points of the plane is a prime. If this order is odd, then it is at most the planar order plus 1.Partially supported by a NSA grant. 相似文献
5.
All known finite generalized quadrangles that admit an automorphism group acting sharply transitively on their point set arise
by Payne derivation from thick elation generalized quadrangles of order s with a regular point. In these examples only two groups occur: elementary abelian groups of even order and odd order Heisenberg
groups of dimension 3. In [2] the authors determined all generalized quadrangles admitting an abelian group with a sharply
transitive point action. Here, we classify thick finite generalized quadrangles admitting an odd order Heisenberg group of
dimension 3 acting sharply transitively on the points. In fact our more general result comes close to a complete solution
of classifying odd order Singer p-groups.
相似文献
6.
Barbu C. Kestenband 《Journal of Geometry》2003,77(1-2):61-101
The polarities of Desarguesian planes have long been known. This author has undertaken to classify
the correlations of finite Desarguesian planes in general. In [6] we have presented all the correlations with identity
companion automorphism which are not polarities, of these planes. In this sequence of papers, we classify the
correlations of planes of order $ p^{2^{i}(2n+1)}, n \neq 0 $, with companion automorphism ( $p^{2^{i}t}$ ), p an odd prime, $ t \neq 0 $.
This represents a complete classification of the correlations of planes of odd nonsquare order (i = 0). Some of
the correlations of planes of odd square order ($ t \neq 0 $ ) are also covered by the present analysis.When the companion automorphism is not trivial, the problem, naturally, becomes more involved, and a great deal
begins to hinge upon the order of the plane being odd or even, and also a square or a nonsquare.The correlations of planes of order $ 2^{2^{i}(2n+1)}, n \neq 0 $, with companion automorphism $ 2^{2^{i}t}, t \neq 0 $, and especially
those of planes of order $ p^{2^{i}(2n+1)}, i \neq 0 $, with companion automorphism $ p^{2^{j}(2r+1)}, j > i $ require a substantially
different treatment, and will be the object of separate efforts. 相似文献
7.
该文给出了三个以 p 群为自同构群的 p6 阶群, 并得到了它们的自同构群的阶. 在这里 p 表示奇素数. 相似文献
8.
Kıvanç Ersoy 《Archiv der Mathematik》2016,106(5):401-407
In this paper, we prove that a finite group with a splitting automorphism of odd order is solvable. By using this result, we prove that a locally finite group with a splitting automorphism of odd order is locally solvable. 相似文献
9.
4p阶群及2p2阶群的自同构群 总被引:3,自引:0,他引:3
黄平安 《纯粹数学与应用数学》2000,16(4):41-46
给出了4p阶群和2p^2阶群的自同构群的结构,这里P是奇素数。 相似文献
10.
11.
Jürgen Eichenauer-Herrmann 《Journal of Computational and Applied Mathematics》1992,40(3):345-349
The inversive congruential method for generating uniform pseudorandom numbers is a particularly attractive alternative to linear congruential generators with their well-known inherent deficiencies like the unfavourable coarse lattice structure in higher dimensions. In the present paper the modulus in the inversive congruential method is chosen as a power of an arbitrary odd prime. The existence of inversive congruential generators with maximal period length is proved by a new constructive characterization of these generators. 相似文献
12.
Ralph Hugh Francis Denniston 《manuscripta mathematica》1973,8(1):21-26
A search has shown that any inversive plane of order 7 must be isomorphic with the Miquelian plane. The method used was explicitly set out in a companion paper, which was concerned with a plane of order 5. 相似文献
13.
Ralph High Francis Denniston 《manuscripta mathematica》1973,8(1):11-19
It is proved that any inversive plane of order 5 must be isomorphic with the Miquelian plane. The proof is given in some detail: a companion paper will assert that the same arguments can be applied to a plane of order 7. 相似文献
14.
In this paper, the subconstituents of the isotropic orthogonal graphs over finite fields of odd characteristic are studied. The first subconstituent is strongly regular, while the second subconstituent is edge-regular. The full automorphism groups of these two subconstituents have also been determined. 相似文献
15.
We investigate automorphism groups of 2-generated quasigroups, constructed in [6], and show that such quasigroups of odd order k ≥ 7 have only one nontrivial automorphism, whereas in the case of even order k ≥ 6 there are no nontrivial automorphisms. 相似文献
16.
Antonio F. Costa 《Proceedings of the American Mathematical Society》1996,124(2):601-605
In this paper we present an example of an anticonformal automorphism whose square has prime order and is not embeddable. We prove that every embeddable automorphism of odd order of a compact Riemann surface is the square of an orientation-reversing self-homeomorphism. Finally we study whether a conformal involution is the square of an orientation-reversing automorphism.
17.
Veerle Fack Svetlana Topalova Joost Winne Rosen Zlatarski 《Discrete Mathematics》2006,306(18):2141-2151
A classification of the doubles of the projective plane of order 4 with respect to the order of the automorphism group is presented and it is established that, up to isomorphism, there are 1 746 461 307 doubles. We start with the designs possessing non-trivial automorphisms. Since the designs with automorphisms of odd prime orders have been constructed previously, we are left with the construction of the designs with automorphisms of order 2. Moreover, we establish that a 2-(21,5,2) design cannot be reducible in two inequivalent ways. This makes it possible to calculate the number of designs with only the trivial automorphism, and consequently the number of all double designs. Most of the computer results are obtained by two different approaches and implementations. 相似文献
18.
This paper is devoted to a study of the automorphism groups of three series of finite-dimensional special odd Hamiltonian superalgebras g over a field of prime characteristic. Our aim is to characterize the connections between the automorphism groups of g and the automorphism groups of the corresponding underlying superalgebras. Precisely speaking, we embed the former into the later. Moreover, we determine the images of the normal series of the automorphism groups and homogeneous automorphism groups of g under the embedded mapping. 相似文献
19.
We show that if U is a Buekenhout-Metz unital (with respect to a point P) in any translation plane of order q
2
with kernel containing GF(q), then U has an associated 2-(q2,q+1,q) design which is the point-residual of an inversive plane, generalizing results of Wilbrink, Baker and Ebert. Further, our proof gives a natural, geometric isomorphism between the resulting inversive plane and the (egglike) inversive plane arising from the ovoid involved in the construction of the Buekenhout-Metz unital. We apply our results to investigate some parallel classes and partitions of the set of blocks of any Buekenhout-Metz unital. 相似文献