Finite soluble groups admitting an automorphism of prime power order with few fixed points
1987 ◽
Vol 102
(3)
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pp. 431-441
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Keyword(s):
Let G be a finite soluble group with Fitting subgroup F(G). The Fitting series of G is defined, as usual, by F0(G) = 1 and Fi(G)/Fi−1(G) = F(G/Fi−1(G)) for i ≥ 1, and the Fitting height h = h(G) of G is the least integer such that Fn(G) = G. Suppose now that a finite soluble group A acts on G. Let k be the composition length of A, that is, the number of prime divisors (counting multiplicities) of |A|. There is a certain amount of evidence in favour of theCONJECTURE. |G:Fk(G)| is bounded by a number depending only on |A| and |CG(A)|.
1969 ◽
Vol 1
(1)
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pp. 3-10
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Keyword(s):
2012 ◽
Vol 56
(1)
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pp. 303-336
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Keyword(s):
Keyword(s):
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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1976 ◽
Vol 19
(2)
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pp. 213-216
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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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Keyword(s):
1973 ◽
Vol 25
(4)
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pp. 862-869
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Keyword(s):
1973 ◽
Vol 16
(3)
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pp. 357-362
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