Bounds on the fitting length of finite soluble groups with supersoluble Sylow normalisers
1991 ◽
Vol 44
(1)
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pp. 19-31
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Keyword(s):
We prove that, in a finite soluble group, all of whose Sylow normalisers are super-soluble, the Fitting length is at most 2m + 2, where pm is the highest power of the smallest prime p dividing |G/Gs| here Gs is the supersoluble residual of G. The bound 2m + 2 is best possible. However under certain structural constraints on G/GS, typical of the small examples one makes by way of experimentation, the bound is sharply reduced. More precisely let p be the smallest, and r the largest, prime dividing the order of a group G in the class under consideration. If a Sylow p–subgroup of G/GS acts faithfully on every r-chief factor of G/GS, then G has Fitting length at most 3.
1976 ◽
Vol 19
(2)
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pp. 213-216
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1969 ◽
Vol 1
(1)
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pp. 3-10
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1974 ◽
Vol 17
(4)
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pp. 385-388
Keyword(s):
1970 ◽
Vol 11
(4)
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pp. 395-400
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2000 ◽
Vol 42
(1)
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pp. 67-74
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Keyword(s):
1972 ◽
Vol 7
(1)
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pp. 101-104
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1987 ◽
Vol 102
(3)
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pp. 431-441
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Keyword(s):
1991 ◽
Vol 51
(2)
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pp. 331-342
Keyword(s):
1979 ◽
Vol 22
(3)
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pp. 191-194
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Keyword(s):
1966 ◽
Vol 62
(3)
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pp. 339-346
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