THE FIXITY OF PERMUTATION-GROUPS

被引：11
作者：
SAXL, J [1 ]
SHALEV, A [1 ]
机构：
[1] HEBREW UNIV JERUSALEM,INST MATH,IL-91904 JERUSALEM,ISRAEL
来源：
JOURNAL OF ALGEBRA | 1995年 / 174卷 / 03期
关键词：
D O I：
10.1006/jabr.1995.1171
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The fixity of a finite permutation group G is the maximal number of fixed points of a non-trivial element of G. We analyze the structure of non-regular permutation groups G with given fixity f. We show that if G is transitive and nilpotent, then it has a subgroup whose index and nilpotency class are both f-bounded. We also show that if G is primitive, then either it has a soluble subgroup of f-bounded index and derived length at most 4, or F*(G) is PSL(2, q) or Sz(q) in the natural permutation representations of degree q + 1, q(2) + 1 respectively. (C) 1995 Academic Press, Inc.
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收藏
页码：1122 / 1140
页数：19
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