Subsets close to invariant subsets for group actions
Authors:
Leonid Brailovsky, Dmitrii V. Pasechnik and Cheryl E. Praeger
Journal:
Proc. Amer. Math. Soc. 123 (1995), 22832295
MSC:
Primary 20B05; Secondary 20B07
MathSciNet review:
1307498
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: Let G be a group acting on a set and k a nonnegative integer. A subset (finite or infinite) is called kquasiinvariant if for every . It is shown that if A is kquasiinvariant for , then there exists an invariant subset such that . Information about Gorbit intersections with A is obtained. In particular, the number m of Gorbits which have nonempty intersection with A, but are not contained in A, is at most . Certain other bounds on , in terms of both m and k, are also obtained.
 [1]
George
M. Bergman and Hendrik
W. Lenstra Jr., Subgroups close to normal subgroups, J.
Algebra 127 (1989), no. 1, 80–97. MR 1029404
(91a:20004), http://dx.doi.org/10.1016/00218693(89)902755
 [2]
B.
J. Birch, R.
G. Burns, Sheila
Oates Macdonald, and Peter
M. Neumann, On the orbitsizes of permutation groups containing
elements separating finite subsets, Bull. Austral. Math. Soc.
14 (1976), no. 1, 7–10. MR 0401882
(53 #5708)
 [3]
L.
Brailovsky, Structure of quasiinvariant sets, Arch. Math.
(Basel) 59 (1992), no. 4, 322–326. MR 1179456
(93h:20016), http://dx.doi.org/10.1007/BF01197046
 [4]
Leonid
Brailovsky, Dmitrii
V. Pasechnik, and Cheryl
E. Praeger, Classification of 2quasiinvariant subsets, Ars
Combin. 42 (1996), 65–76. MR 1386928
(97a:05204)
 [5]
P.
Dembowski, Finite geometries, Ergebnisse der Mathematik und
ihrer Grenzgebiete, Band 44, SpringerVerlag, BerlinNew York, 1968. MR 0233275
(38 #1597)
 [6]
P.
Erdős, Chao
Ko, and R.
Rado, Intersection theorems for systems of finite sets, Quart.
J. Math. Oxford Ser. (2) 12 (1961), 313–320. MR 0140419
(25 #3839)
 [7]
P. Frankl and Z. Füredi, Nontrivial intersecting families, J. Combin. Theory Ser. A 41 (1986), 150153.
 [8]
B.
H. Neumann, Groups covered by permutable subsets, J. London
Math. Soc. 29 (1954), 236–248. MR 0062122
(15,931b)
 [9]
Cheryl
E. Praeger, On permutation groups with bounded movement, J.
Algebra 144 (1991), no. 2, 436–442. MR 1140614
(93a:20003), http://dx.doi.org/10.1016/00218693(91)90114N
 [1]
 G.M. Bergman and H.W. Lenstra, Jr., Subgroups close to normal subgroups, J. Algebra 127 (1989), 8097. MR 1029404 (91a:20004)
 [2]
 B.J. Birch, R.G. Burns, S. Oates Macdonald, and P.M. Neumann, On the orbitsizes of permutation groups containing elements separating finite subsets, Bull. Austral. Math. Soc. 14 (1976), 710. MR 0401882 (53:5708)
 [3]
 L. Brailovsky, Structure of quasiinvariant sets, Arch. Math. (Basel) 59 (1992), 322326. MR 1179456 (93h:20016)
 [4]
 L. Brailovsky, D.V. Pasechnik, and C.E. Praeger, Classification of 2quasiinvariant sets, Ars Combin. (to appear). MR 1386928 (97a:05204)
 [5]
 P. Dembowski, Finite geometries, SpringerVerlag, New York, 1968. MR 0233275 (38:1597)
 [6]
 P. Erdös, C. Ko, and R. Rado, Intersection theorems for systems of finite sets, Quart. J. Math. Oxford Ser. (2) 12 (1961), 313320. MR 0140419 (25:3839)
 [7]
 P. Frankl and Z. Füredi, Nontrivial intersecting families, J. Combin. Theory Ser. A 41 (1986), 150153.
 [8]
 B.H. Neumann, Groups covered by permutable subsets, J. London Math. Soc. (2) 29 (1954), 236248. MR 0062122 (15:931b)
 [9]
 C.E. Praeger, On permutation groups with bounded movement, J. Algebra 44 (1991), 436442. MR 1140614 (93a:20003)
Similar Articles
Retrieve articles in Proceedings of the American Mathematical Society
with MSC:
20B05,
20B07
Retrieve articles in all journals
with MSC:
20B05,
20B07
Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939199513074983
PII:
S 00029939(1995)13074983
Article copyright:
© Copyright 1995
American Mathematical Society
