共查询到20条相似文献,搜索用时 15 毫秒
1.
Barbara Priwitzer 《Monatshefte für Mathematik》1999,127(1):67-82
This paper deals with the so-called Salzmann program aiming to classify special geometries according to their automorphism
groups. Here, topological connected compact projective planes are considered. If finite-dimensional, such planes are of dimension
2, 4, 8, or 16. The classical example of a 16-dimensional, compact projective plane is the projective plane over the octonions
with 78-dimensional automorphism group E6(−26). A 16-dimensional, compact projective plane ? admitting an automorphism group of dimension 41 or more is clasical, [23]
87.5 and 87.7. For the special case of a semisimple group Δ acting on ? the same result can be obtained if dim , see [22]. Our aim is to lower this bound. We show: if Δ is semisimple and dim , then ? is either classical or a Moufang-Hughes plane or Δ is isomorphic to Spin9 (ℝ, r), r∈{0, 1}. The proof consists of two parts. In [16] it has been shown that Δ is in fact almost simple or isomorphic to SL3?ċSpin3ℝ. In the underlying paper we can therefore restrict our considerations to the case that Δ is almost simple, and the corresponding
planes are classified.
Received 10 February 1997; in final form 19 December 1997 相似文献
2.
Barbara Priwitzer 《Monatshefte für Mathematik》1999,68(5):67-82
This paper deals with the so-called Salzmann program aiming to classify special geometries according to their automorphism
groups. Here, topological connected compact projective planes are considered. If finite-dimensional, such planes are of dimension
2, 4, 8, or 16. The classical example of a 16-dimensional, compact projective plane is the projective plane over the octonions
with 78-dimensional automorphism group E6(−26). A 16-dimensional, compact projective plane ? admitting an automorphism group of dimension 41 or more is clasical, [23]
87.5 and 87.7. For the special case of a semisimple group Δ acting on ? the same result can be obtained if dim , see [22]. Our aim is to lower this bound. We show: if Δ is semisimple and dim , then ? is either classical or a Moufang-Hughes plane or Δ is isomorphic to Spin9 (ℝ, r), r∈{0, 1}. The proof consists of two parts. In [16] it has been shown that Δ is in fact almost simple or isomorphic to SL3?ċSpin3ℝ. In the underlying paper we can therefore restrict our considerations to the case that Δ is almost simple, and the corresponding
planes are classified. 相似文献
3.
Cornelia Rößing 《Journal of Geometry》2009,91(1-2):140-149
4.
Hermann Hähl 《Geometriae Dedicata》2000,83(1-3):105-117
The 16-dimensional compact projective planes whose automorphism group contains a closed connected subgroup fixing a line, but no point and having dimension at least 35 are determined. It is shown that these planes all belong to three families of planes determined by H. Löwe and the author, and hence are explicitly known. A major stepping stone to this goal is a result by H. Salzmann according to which every such plane is a translation plane. 相似文献
5.
Coleman自同构群的投射极限 总被引:2,自引:0,他引:2
在这篇注记中,利用群的投射极限性质给出了有限可解群的Coleman自同构群的一个具体构造.作为应用,证明了二面体群的Coleman外自同构群或者是1或者是一个初等阿贝尔2-群. 相似文献
6.
Coleman自同构群的投射极限 总被引:1,自引:1,他引:0
在这篇注记中,利用群的投射极限性质给出了有限可解群的Coleman自同构群的一个具体构造.作为应用,证明了二面体群的Coleman外自同构群或者是1或者是一个初等阿贝尔2-群. 相似文献
7.
设G是有限群,H(?)G。如果H≌~2B_2(q)或H≌~2G_2(q)或H≌PSU(3,q),则G不与任何射影平面的点传递直射群同均。本文对以下问题给出了一般方法:证明以某些几乎单群为点传递自同构群的线性空间不是射影平面。 相似文献
8.
Günter F. Steinke 《Monatshefte für Mathematik》2002,136(4):327-354
This paper concerns 4-dimensional (topological locally compact connected) elation Laguerre planes that admit non-solvable
automorphism groups. It is shown that such a plane is either semi-classical or a single plane admitting the group SL(2, ). Various characterizations of this single Laguerre plane are obtained.
Received October 17 2000; in revised form April 23 2001 Published online August 5, 2002 相似文献
9.
Hauke Klein 《Results in Mathematics》1995,28(1-2):100-116
We consider a 4-dimensional compact projective plane $\pi = ({\cal P},{\cal L})$ ?e whose collineation group σ is 6-dimensional and solvable with a 4-dimensional nilradical N. We assume that σ fixes a flag υ ∈ W, acts transitively on ${\cal L}_{\upsilon}\setminus \lbrace W \rbrace$ ?e, and fixes no point in the set W{υ}. If π is neither a translation plane nor a dual translation plane, nor a shift plane, then we will show that ?(N) ? nil × R, i.e. the local structure of N is uniquely determined. 相似文献
10.
Hauke Klein 《Geometriae Dedicata》1999,77(3):271-277
We consider a four-dimensional compact projective plane
whose collineation group is six-dimensional and solvable with a nilradical N isomorphic to Nil×R, where Nil denotes the three-dimensional, simply connected, non-Abelian, nilpotent Lie group. We assume that fixes a flag p W, acts transitively on
and fixes no point in the set W\p. Under these conditions, we will prove that either contains a three-dimensional group of elations or acts doubly transitively on
. 相似文献
11.
We consider 4-dimensional flexible projective planes with the following properties: The collineation group is a 6-dimensional solvable Lie group which fixes some flag ∞ ∈ W. Furthermore, the collineation group has a 1-dimensional orbit both on W and on the pencil of lines through {∞}. We show that there are three different families of planes with these properties. 相似文献
12.
Richard Bödi 《Geometriae Dedicata》1998,72(3):283-297
Smooth projective planes are projective planes defined on smooth manifolds (i.e. the set of points and the set of lines are smooth manifolds) such that the geometric operations of join and intersection are smooth. A systematic study of such planes and of their collineation groups can be found in previous works of the author. We prove in this paper that a 16-dimensional smooth projective plane which admits a collineation group of dimension d 39 is isomorphic to the octonion projective plane P2 O. For topological compact projective planes this is true if d 41. Note that there are nonclassical topological planes with a collineation group of dimension 40. 相似文献
13.
GÜnter F. Steinke 《Results in Mathematics》1994,26(1-2):131-142
This paper concerns 2-dimensional (topological locally compact connected) Minkowski planes. It uses a construction of J. Jakóbowski [4] of Minkowski planes over half-ordered fields and applies it to the field of reals. This generalizes a construction by A. Schenkel [7] of 2-dimensional Minkowski planes admitting a 3-dimensional kernel. It is shown that most planes in this family of Minkowski planes have 0-dimensional and even trivial automorphism groups. 相似文献
14.
If G is a finite group and if A is a group of automorphisms of G whose fixed point subgroup is C
G
(A) then every subgroup F of C
G
(A) acts on the set of orbits of A in G. The peculiarities of this action are used here to derive several results on the number of orbits of A in an economical manner.Original Russian Text Copyright © 2005 Deaconescu M. and Walls G. L.__________Translated from Sibirskii Matematicheskii Zhurnal, Vol. 46, No. 3, pp. 533–537, May–June, 2005. 相似文献
15.
Using symplectic topology and the Radon transform, we prove that smooth 4-dimensional projective planes are diffeomorphic
to
. We define the notion of a plane curve in a smooth projective plane, show that plane curves in high dimensional regular planes
are lines, prove that homeomorphisms preserving plane curves are smooth collineations, and prove a variety of results analogous
to the theory of classical projective planes.
*Thanks to Robert Bryant and John Franks. 相似文献
16.
The Gruenberg–Kegel graph GK(G) = (V G , E G ) of a finite group G is a simple graph with vertex set V G = π(G), the set of all primes dividing the order of G, and such that two distinct vertices p and q are joined by an edge, {p, q} ∈ E G , if G contains an element of order pq. The degree deg G (p) of a vertex p ∈ V G is the number of edges incident to p. In the case when π(G) = {p 1, p 2,…, p h } with p 1 < p 2 < … <p h , we consider the h-tuple D(G) = (deg G (p 1), deg G (p 2),…, deg G (p h )), which is called the degree pattern of G. The group G is called k-fold OD-characterizable if there exist exactly k non-isomorphic groups H satisfying condition (|H|, D(H)) = (|G|, D(G)). Especially, a 1-fold OD-characterizable group is simply called OD-characterizable. In this paper, we prove that the simple groups L 10(2) and L 11(2) are OD-characterizable. It is also shown that automorphism groups Aut(L p (2)) and Aut(L p+1(2)), where 2 p ? 1 is a Mersenne prime, are OD-characterizable. Finally, a list of finite (simple) groups which are presently known to be k-fold OD-characterizable, for certain values of k, is presented. 相似文献
17.
Mathematical Notes - 相似文献
18.
C. Herrmann 《Acta Mathematica Hungarica》1998,79(1-2):35-38
Every (finite) group is isomorphic to the automorphism group of some (finite) subdirectly irreducible Arguesian lattice. 相似文献
19.
Hou-Yi Chen 《代数通讯》2013,41(1):263-266
Let X be a smooth complex projective 3-fold of general type. We give effective upper bounds for the order of the automorphism group of X under certain conditions. 相似文献
20.
William M. Kantor 《Journal of Algebraic Combinatorics》1994,3(4):405-425
Translation planes of order q are constructed whose full collineation groups have order q
2. 相似文献