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Transitivity of finite permutation groups on unordered sets

โœ Scribed by Donald Livingstone; Ascher Wagner

Publisher
Springer-Verlag
Year
1965
Tongue
French
Weight
574 KB
Volume
90
Category
Article
ISSN
0025-5874

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๐Ÿ“œ SIMILAR VOLUMES

Permutation groups on unordered sets
Permutation groups on unordered sets
โœ Ronald D. Bercov; Charles R. Hobby ๐Ÿ“‚ Article ๐Ÿ“… 1970 ๐Ÿ› Springer-Verlag ๐ŸŒ French โš– 243 KB
Permutation groups on unordered sets II;
Permutation groups on unordered sets II; On a theorem of Frucht
โœ Johannes Siemons ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 289 KB

We show that every group is the full automorphism group of an unordered k-relation for given k 2 2 on some suitable set. We are also concerned with the cardinality of a minimal representation with this property as a function of k.

On Permutation Groups of Finite Type
On Permutation Groups of Finite Type
โœ Clara Franchi ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 213 KB

A permutation group G is said to be a group of finite type {k}, k a positive integer, if each nonidentity element of G has exactly k fixed points. We show that a group G can be faithfully represented as an irredundant permutation group of finite type if and only if G has a non-trivial normal partiti