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We show that every element of PSL(2, q) is a commutator of elements of coprime orders. This is proved by showing first that in PSL(2, q) any two involutions are conjugate by an element of odd order.  相似文献   

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For an odd prime p?≠ 7, let q be a power of p such that ${q^3\equiv1 \pmod 7}$ . It is known that the desarguesian projective plane PG(2, q) of order q has a unique conjugacy class of projectivity groups isomorphic to PSL(2, 7). For such a projective group Γ, we investigate the geometric properties of the (unique) Γ-orbit Ω of size 42 such that the 1-point stabilizer of Γ in Ω is a cyclic group of order 4. We present a computational approach to prove that Ω is a 42-arc provided that q?≥ 53 and q?≠ 373, 116, 56, 36. We discuss the case q?=?53 in more detail showing the completeness of Ω for q?=?53.  相似文献   

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2-(v,k,1)设计和PSL(3,q)(q是奇数)   总被引:1,自引:0,他引:1  
§ 1  IntroductionA2 -(v,k,1 ) design D=(S,B) consists ofa finite set Sof v points and a collection Bof some subsets of S,called blocks,such that any two points lie on exactly one blockand each block contains exactly k points.A flag of Dis a pair(α,B) such thatα∈S,B∈Bandα∈B,the set of all flags is denoted by F.We assume that2≤k≤v.An automorphism of Dis a permutation of the points which leaves the set Binvari-ant,all the automorphisms form a group Aut D.Let G be a subgroup of A…  相似文献   

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Non-abelian simple totally irregular collineation groups containing an involutorial perspectivity have been classified by the authors in a recent paper. They are PSL(2,q), PSL(3,q), PSU(3,q), Sz(q), the alternating group on 7 letters, and the second Janko sporadic simple group. In this article, we study PSL(2,q),q congruent to 1 modulo 4, as a collineation group containing an involutory homology.C. Y. Ho was partially supported by a NSA grant.  相似文献   

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In this paper we are interested in triangle groups (j, k, l) where j = 2 and k = 3. The groups (j, k, l) can be considered as factor groups of the modular group PSL(2, Z) which has the presentation x, y : x2 = y3 = 1. Since PSL(2,q) is a factor group of Gk,l,m if -1 is a quadratic residue in the finite field Fq, it is therefore worthwhile to look at (j, k, l) groups as subgroups of PSL(2, q) or PGL(2, q). Specifically, we shall find a condition in form of a polynomial for the existence of groups (2, 3, k) as subgroups of PSL(2, q) or PGL(2, q).Mathematics Subject Classification: Primary 20F05 Secondary 20G40.  相似文献   

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《代数通讯》2013,41(6):2325-2339
Abstract

Order components of a finite group are introduced in Chen [Chen, G. Y. (1996c) On Thompson's conjecture. J. Algebra 185:184–193]. It was proved that PSL(3, q), where q is an odd prime power, is uniquely determined by its order components [Iranmanesh, A., Alavi, S. H., Khosravi, B. (2002a). A characterization of PSL(3, q) where q is an odd prime power. J. Pure Appl. Algebra 170(2–3): 243–254]. Also in Iranmanesh et al. [Iranmanesh, A., Alavi, S. H., Khosravi, B. (2002b). A characterization of PSL(3, q) where q = 2 n . Acta Math. Sinica, English Ser. 18(3):463–472] and [Iranmanesh, A., Alavi, S. H. (2002). A characterization of simple groups PSL(5, q). Bull. Austral. Math. Soc. 65:211–222] it was proved that PSL(3, q) for q = 2 n and PSL(5, q) are uniquely determined by their order components. In this paper we prove that PSL(p, q) can be uniquely determined by its order components, where p is an odd prime number. A main consequence of our results is the validity of Thompson's conjecture for the groups under consideration.  相似文献   

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We give three definitions of the Coxeter graph. By the second one we see that PSL(2, 7) is contained in the automorphism group of that graph as a subgroup of index 2, and by the third one that the same holds for PSL(3, 2).  相似文献   

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Let q be a power of 2 greater than 2 and consider the group G = PSL2(q). We choose the maximal subgroups of G isomorphic to the dihedral groups D2(q+1) and D2(q-1) and present the primitive action of G on the right cosets of these two subgroups. We will find the orbits of the point stabilizer in each case and in the case of D2(q-1) we will prove there is an orbit Δ of the point stabilizer Gω, such that Δ ≠ {ω } and whose orbiting under G gives a 1-design with the automorphism group isomorphic to the symmetric group   相似文献   

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This article is a contribution to the study of the automorphism groups of 3-(v,k,3) designs.Let S =(P,B) be a non-trivial 3-(q+ 1,k,3) design.If a two-dimensional projective linear group PSL(2,q) acts flag-transitively on S,then S is a 3-(q + 1,4,3) or 3-(q + 1,5,3) design.  相似文献   

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Jamshid Moori 《代数通讯》2018,46(1):160-166
In this paper, we use Key-Moori methods 1 and 2 to construct some designs from the maximal subgroups and conjugacy classes of the group PSL2(q), where q is a power of 2.  相似文献   

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Ari Vesanen 《代数通讯》2013,41(4):1177-1195
ABSTRACT

We introduce the notion of weak transitivity for torsion-free abelian groups. A torsion-free abelian group G is called weakly transitive if for any pair of elements x, y ∈ G and endomorphisms ?, ψ ∈ End(G) such that x? = y, yψ = x, there exists an automorphism of G mapping x onto y. It is shown that every suitable ring can be realized as the endomorphism ring of a weakly transitive torsion-free abelian group, and we characterize up to a number-theoretical property the separable weakly transitive torsion-free abelian groups.  相似文献   

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Let Π be a projective plane of order n admitting a collineation group G≅PSL(2, q) for some prime power q. It is well known for n=q that Π must be Desarguesian. We show that if n<q then only finitely many cases may occur for П, all of which are Desarguesian. We obtain some information in case n=q 2 with q odd, notably that G acts irreducibly on П for q≠3, 5, 9. The material herein was presented to the University of Toronto in partial fulfillment of the requirements for the degree of Doctor of Philosophy. The author is grateful to Professor Chat Y. Ho, presently at the University of Florida, for guidance in this research.  相似文献   

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