Section graphs for finite permutation groups
نویسندگان
چکیده
منابع مشابه
Finite Transitive Permutation Groups and Finite Vertex-Transitive Graphs
The theory of vertex-transitive graphs has developed in parallel with the theory of transitive permutation groups. In this chapter we explore some of the ways the two theories have influenced each other. On the one hand each finite transitive permutation group corresponds to several vertex-transitive graphs, namely the generalised orbital graphs which we shall discuss below. On the other hand, ...
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In the past two decades, there have been far-reaching developments in the problem of determining all finite non-abelian simple groups—so much so, that many people now believe that the solution to the problem is imminent. And now, as I correct these proofs in October 1980, the solution has just been announced. Of course, the solution will have a considerable effect on many related areas, both wi...
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1. Dejter, I., Giudici, R.E.: On Unitary Cayley graphs, JCMCC, 18,121-124. 2. Brrizbitia, P and Giudici, R.E. 1996, Counting pure k-cycles in sequence of Cayley graphs, Discrete math., 149, 11-18. 3. Madhavi, L and Maheswari, B.2009, Enumeration of Triangles and Hamilton Cycles in Quadratic residue Cayley graphas, Chamchuri Journal of Mathematics, 1,95-103. 4. Madhavi, L and Maheswari, B. 2010,...
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1 Multiply transitive groups Theorem 1.1. Let Ω be a finite set and G ≤ Sym(Ω) be 2–transitive. Let N E G be a minimal normal subgroup. Then one of the following holds: (a) N is regular and elementary abelian. (b) N is primitive, simple and not abelian. Proof. First we show that N is unique. Suppose that M is another minimal normal subgroup of G, so N ∩M = {e} and therefore [N,M ] = {e}. Since ...
متن کاملIntersection Matrices for Finite Permutation Groups*
In this paper we study finite transitive groups G acting on a set Q. The results, which are trivial for multiply-transitive groups, directly generalize parts of the discussion of rank-3 groups in [4] and [5l. There arc close connections with Feit and Higman’s paper [2]. For each a EQ let us choose a G,-orbit d(a) # {CZ} so that d(a)8 = d(a”) for all a E Sz and g E G. Relative to LI we introduce...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory
سال: 1969
ISSN: 0021-9800
DOI: 10.1016/s0021-9800(69)80034-7