TY - JOUR
T1 - Cofinitary permutation groups
AU - Cameron, Peter J.
PY - 1996/1/1
Y1 - 1996/1/1
N2 - A permutation group is cofinitary if any non-identity element fixes only finitely many points. This paper presents a survey of such groups. The paper has four parts. Sections 1-6 develop some basic theory, concerning groups with finite orbits, topology, maximality, and normal subgroups. Sections 7-12 give a variety of constructions, both direct and from geometry, combinatorial group theory, trees, and homogeneous relational structures. Sections 13-15 present some generalisations of sharply k-transitive groups, including an orbit-counting result with a character-theoretic flavour. The final section treats some miscellaneous topics. Several open problems are mentioned.
AB - A permutation group is cofinitary if any non-identity element fixes only finitely many points. This paper presents a survey of such groups. The paper has four parts. Sections 1-6 develop some basic theory, concerning groups with finite orbits, topology, maximality, and normal subgroups. Sections 7-12 give a variety of constructions, both direct and from geometry, combinatorial group theory, trees, and homogeneous relational structures. Sections 13-15 present some generalisations of sharply k-transitive groups, including an orbit-counting result with a character-theoretic flavour. The final section treats some miscellaneous topics. Several open problems are mentioned.
UR - http://www.scopus.com/inward/record.url?scp=0001358827&partnerID=8YFLogxK
U2 - 10.1112/blms/28.2.113
DO - 10.1112/blms/28.2.113
M3 - Article
AN - SCOPUS:0001358827
SN - 0024-6093
VL - 28
SP - 113
EP - 140
JO - Bulletin of the London Mathematical Society
JF - Bulletin of the London Mathematical Society
IS - 2
ER -