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Point-symmetric graphs and digraphs of prime order and transitive permutation groups of prime degree
Brian Alspach 《Journal of Combinatorial Theory, Series B》1973,15(1):12-17
In this paper the following two problems are solved: Given any point-symmetric graph or digraph Γ of prime order the automorphism group of Γ is explicitly determined and given any transitive permutation group G of prime degree p the number of digraphs and graphs of order p having G as their automorphism group is determined. 相似文献
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Michael Woltermann 《代数通讯》2013,41(17):1877-1883
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In [ 3 ] M. D. Atkinson conjectured that if G is a doubly transitive but not doubly primitive permutation group on Ω, then G is of one of the following four types: i) Metacyclic groups of prime degree p and of order p(p -1); ii) Groups of degree 2p and of order 2p(2p-1)or 2p(2p-l)p for some prime p;iii)Gr-oups of automorphisms of a block design with λ=1; iv) Sz(q)≤G≤Aut(Sz(g)).In this paper we proved this conjecture in a special case without using the result of classification of finte simple groups, Qur explicit result is as follows: Theorem. Let G be a doubly transitive group on set Ω,where |Ω|=6q+1 and q is a prime, then one of the following holds: i)G is doubly primitive on Ω;ii) G is sharply doubly transitive on Ω; iii) G is a groups of automorphisms of a block design with λ=1. 相似文献
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Part of this work was done while the author was the recipient of RGC Grant 1423 awarded by the University of Alabama Research Grants Committee. 相似文献
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M. Kuzucuoğlu 《Journal of Mathematical Sciences》2013,195(4):486-486
We study some properties for barely transitive group. 相似文献
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William M. Kantor 《Israel Journal of Mathematics》1974,18(2):141-143
The groups in the title are classified, provided they are not too highly transitive.
This research was supported in part by NSF Grant GP 37982X. 相似文献
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Let G be a doubly but not triply transitive group on a set X. We give an algorithm to construct the orbits of G acting on X×X×X by combining those of its stabilizer H of a point of X If the group H is given first, we compute the orbits of its transitive extension G, if it exists. We apply our algorithm to G=PSL(m,q) and Sp(2m,2), m3, successfully. We go forward to compute the transitive extension of G itself. In our construction we use a superscheme defined by the orbits of H on X×X×X and do not use group elements. 相似文献
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We investigate properties of finite transitive permutation groups in which all proper subgroups of G act intransitively on . In particular, we are interested in reduction theorems for minimally transitive representations of solvable groups.
Work partially supported by M.I.U.R. and London Mathematical Society. 相似文献
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David Chillag 《Israel Journal of Mathematics》1973,15(1):78-91
SupposeG is a nonsolvable transitive permutation group of prime degreep, such that |N
G
v(P)|=p(p−1) for some Sylowp-subgroupP ofG. Letq be a generator of the subgroup ofN
G
(P), fixing one letter (it is easy to show that this subgroup is cyclic). Assume thatG contains an elementj such thatj
−1
qj=q
(p+1)/2. We shall prove that for almost all primesp of the formp=4n+1, a group that satisfies the above conditions must be the symmetric group on a set withp elements. 相似文献
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The structure of transitive ordered permutation groups 总被引:3,自引:0,他引:3
We give some necessary and sufficient conditions for transitive l-permutation groups to be 2-transitive. We also discuss primitive components and give necessary and sufficient conditions for transitive l-permutation groups to be normal-valued. 相似文献
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I. M. Isaacs 《Proceedings of the American Mathematical Society》2002,130(7):1923-1925
In this note we prove that if the point stabilizer in a transitive permutation group of degree is abelian, then the exponent of is less than . This extends an earlier result of Andrea Lucchini, who proved this in the case where is cyclic.