李慧陵,沈虹.6q+1级2—传递置换群,q为素数[J].数学研究及应用,1986,6(1):55~61
6q+1级2—传递置换群,q为素数
Deubly transitive permutation groups of degree 6q + 1, q being a prime
投稿时间:1982-02-12  
DOI:10.3770/j.issn:1000-341X.1986.01.016
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李慧陵 兰州大学 
沈虹 西安工业学院 
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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.
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