Sylow subgroups of transitive permutation groups II
1977 ◽
Vol 23
(3)
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pp. 329-332
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Keyword(s):
AbstractLet G be a transitive permutation group on a finite set of n points, and let P be a Sylow p-subgroup of G for some prime p dividing |G|. We are concerned with finding a bound for the number f of points of the set fixed by P. Of all the orbits of P of length greater than one, suppose that the ones of minimal length have length q, and suppose that there are k orbits of P of length q. We show that f ≦ kp − ip(n), where ip(n) is the integer satisfying 1 ≦ ip(n) ≦ p and n + ip(n) ≡ 0(mod p). This is a generalisation of a bound found by Marcel Herzog and the author, and this new bound is better whenever P has an orbit of length greater than the minimal length q.
2002 ◽
Vol 65
(2)
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pp. 277-288
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1984 ◽
Vol 36
(1)
◽
pp. 69-86
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1976 ◽
Vol 21
(4)
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pp. 428-437
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Keyword(s):
1978 ◽
Vol 18
(3)
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pp. 465-473
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1989 ◽
Vol 40
(2)
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pp. 255-279
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1977 ◽
Vol 23
(2)
◽
pp. 202-206
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1978 ◽
Vol 25
(2)
◽
pp. 145-166
1966 ◽
Vol 27
(1)
◽
pp. 159-169
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