this paper is dedicated to helmut wielandt on the occasion of his 90th birthday Let A be a transitive subgroup of S n . We show that the largest cyclic quotient of A has order at most n. This can be interpreted as an equivalent result about extensions of constants in the Galois closure of a coverin
Characterization of Certain 2-Transitive Groups
β Scribed by T. Peterfalvi
- Publisher
- Elsevier Science
- Year
- 1994
- Tongue
- English
- Weight
- 357 KB
- Volume
- 164
- Category
- Article
- ISSN
- 0021-8693
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π SIMILAR VOLUMES
A directed graph is called (m, k)-transitive if for every directed path x0x1 . ..x. there is a directed path y,y, . ..yt such that x0 =y ,,, x,=yl,, and {yiIO<iik}c{xiIO<i<m}. We describe the structure of those (m, 1)-transitive and (3,2)-transitive directed graphs in which each pair of vertices is
For a permutation group G on a set S, the mo¨ement of G is defined as the maximum cardinality of subsets T of S for which there exists an element x g G x Ž such that T is disjoint from its translate T that is, when such subsets have . bounded cardinality . It was shown by the second author that, if
to helmut wielandt on the occasion of his 90th birthday We investigate the finite primitive permutation groups G which have a transitive subgroup containing no nontrivial subnormal subgroup of G. The conclusion is that such primitive groups are rather rare, and that their existence is intimately co