Intersection matrices for finite permutation groups
نویسندگان
چکیده
منابع مشابه
Intersection 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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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 ...
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By the Artin Induction theorem,C(G) is a finite abelian group with exponent dividing the order of G. Some work on this sequence has already been done. In [14] and [16], Ritter and Segal proved that C(G) = 0 for G a finite p–group. Serre [17, p. 104] remarked that C(G) / = 0 for G = Z/3 × Q8 (the direct product of a cyclic group of order 3 and a quaternion group of order 8). Berz [2] gave a nice...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1967
ISSN: 0021-8693
DOI: 10.1016/0021-8693(67)90011-7