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Mutually Permutable Products of Finite Groups

✍ Scribed by A. Ballester-Bolinches; M.D. Pérez-Ramos; M.C. Pedraza-Aguilera


Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
76 KB
Volume
213
Category
Article
ISSN
0021-8693

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Sylow Permutable Subnormal Subgroups of
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A finite group G is said to be a PST -group if every subnormal subgroup of G permutes with every Sylow subgroup of G. We shall discuss the normal structure of soluble PST -groups, mainly defining a local version of this concept. A deep study of the local structure turns out to be crucial for obtaini

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Let G be a permutation group of finite degree d. We prove that the product of the orders of the composition factors of G that are not alternating groups acting naturally, in a sense that will be made precise, is bounded by c d-1 /d, where c = 4 5. We use this to prove that any quotient G/N of G has