Orbit-equivalent infinite permutation groups

被引：1

作者：

Lockett, D. C. ^{[1
]}

Macpherson, H. D. ^{[1
]}

机构：

[1] Univ Leeds, Sch Math, Leeds LS2 9JT, W Yorkshire, England

来源：

JOURNAL OF ALGEBRAIC COMBINATORICS | 2013年 / 38卷 / 04期

基金：

英国工程与自然科学研究理事会;

关键词：

Primitive permutation group; Orbit-equivalent; Set-homogeneous; NO REGULAR ORBITS; HOMOGENEOUS GRAPHS; UNORDERED SETS; SUBSETS;

D O I：

10.1007/s10801-013-0434-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G,H be closed permutation groups on an infinite set X, with H a subgroup of G. It is shown that if G and H are orbit-equivalent, that is, have the same orbits on the collection of finite subsets of X, and G is primitive but not 2-transitive, then G=H.

引用

页码：973 / 988

页数：16

共 50 条

[41] PRIMITIVE PERMUTATION GROUPS WITH A DOUBLY TRANSITIVE SUB-ORBIT
PRAEGER, CE
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1978, 17 (FEB): : 67 - 73
[42] A property equivalent to n-permutability for infinite groups
Abdollahi, A
Hassanabadi, AM
Taeri, B
[J]. JOURNAL OF ALGEBRA, 1999, 221 (02) : 570 - 578
[43] GROWTH-RATES IN INFINITE-GRAPHS AND PERMUTATION-GROUPS
MACPHERSON, HD
[J]. PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1985, 51 (SEP) : 285 - 294
[44] INFINITE PERMUTATION-GROUPS .1. PRODUCTS OF CONJUGACY CLASSES
TRUSS, JK
[J]. JOURNAL OF ALGEBRA, 1989, 120 (02) : 454 - 493
[45] INFINITE PERMUTATION-GROUPS .2. SUBGROUPS OF SMALL INDEX
TRUSS, JK
[J]. JOURNAL OF ALGEBRA, 1989, 120 (02) : 494 - 515
[46] NORMAL-SUBGROUPS OF INFINITE MULTIPLY TRANSITIVE PERMUTATION-GROUPS
CAMERON, PJ
[J]. COMBINATORICA, 1981, 1 (04) : 343 - 347
[47] A NOTE ON CERTAIN PERMUTATION-GROUPS IN THE INFINITE DIMENSIONAL ROTATION GROUP
OBATA, N
[J]. NAGOYA MATHEMATICAL JOURNAL, 1988, 109 : 91 - 107
[48] Infinite commensurable hyperbolic groups are bi-Lipschitz equivalent
Bogopolskii O.V.
[J]. Algebra and Logic, 1997, 36 (3) : 155 - 163
[49] Primitive permutation groups satisfying the small orbit property and a problem of Bourgain and Kalai
Benbenisty, Carmit
[J]. JOURNAL OF ALGEBRAIC COMBINATORICS, 2019, 50 (02) : 225 - 235
[50] Primitive permutation groups satisfying the small orbit property and a problem of Bourgain and Kalai
Carmit Benbenisty
[J]. Journal of Algebraic Combinatorics, 2019, 50 : 225 - 235

← 1 2 3 4 5 →