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On permutation groups with bounded movement

✍ Scribed by Cheryl E. Praeger

Publisher
Elsevier Science
Year
1991
Tongue
English
Weight
399 KB
Volume
144
Category
Article
ISSN
0021-8693

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πŸ“œ SIMILAR VOLUMES

Transitive Permutation Groups with Bound
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Let G be a transitive permutation group on a set ⍀ such that G is not a 2-group and let m be a positive integer. It was shown by the fourth author that if < g < < < ? Ε½ . @ ⌫ \_ ⌫ F m for every subset ⌫ of ⍀ and all g g G, then ⍀ F 2 mpr p y 1 , < < < < where p is the least odd prime dividing G . If

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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

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Certain groups with bounded movement hav
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✍ Pan Soo Kim; Yangkok Kim πŸ“‚ Article πŸ“… 2002 πŸ› Elsevier Science 🌐 English βš– 90 KB

Let G be a permutation group on a set Ω such that G has no fixed points in Ω. If, for a given positive integer m, the cardinalities |Ξ“ g \Ξ“ | is at most m for all g ∈ G and Ξ“ βŠ† Ω, then G is said to have bounded movement m on Ω. When the maximum of |Ξ“ g \Ξ“ | over all g ∈ G and Ξ“ βŠ† Ω is equal to m, we