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An inequality for finite permutation groups

✍ Scribed by Masao Kiyota


Publisher
Elsevier Science
Year
1979
Tongue
English
Weight
44 KB
Volume
27
Category
Article
ISSN
0097-3165

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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

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A group G is a PT -group if, for subgroups H and K with H permutable in K and K permutable in G, it is always the case that H is permutable in G. It is shown that a finite group is a soluble PT -group if and only if each subgroup of a Sylow subgroup is permutable in the Sylow normalizer.