ORCID Profile
0000-0003-0035-8662
Current Organisation
University of Lincoln
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Publisher: Springer Science and Business Media LLC
Date: 19-07-2014
Publisher: Walter de Gruyter GmbH
Date: 03-2012
DOI: 10.1515/JGT.2011.108
Abstract: If is a group of permutations of a set , then the suborbits of are the orbits of point-stabilizers acting on . The cardinalities of these suborbits are the subdegrees of . Every infinite primitive permutation group with finite subdegrees acts faithfully as a group of automorphisms of a locally-finite connected vertex-primitive directed graph with vertex set , and there is consequently a natural action of on the ends of . We show that if is closed in the permutation topology of pointwise convergence, then the structure of is determined by the length of any orbit of acting on the ends of . Examining the ends of a Cayley graph of a finitely-generated group to determine the structure of the group is often fruitful. B. Krön and R. G. Möller have recently generalised the Cayley graph to what they call a rough Cayley graph , and they call the ends of this graph the rough ends of the group. It transpires that the ends of are the rough ends of , and so our result is equivalent to saying that the structure of a closed primitive group whose subdegrees are all finite is determined by the length of any orbit of on its rough ends.
Publisher: Springer Science and Business Media LLC
Date: 28-07-2009
Publisher: Elsevier BV
Date: 06-2015
Publisher: Duke University Press
Date: 15-10-2017
Publisher: Springer Science and Business Media LLC
Date: 29-05-2014
Publisher: Elsevier BV
Date: 10-2020
Publisher: Walter de Gruyter GmbH
Date: 20-01-2007
DOI: 10.1515/JGT.2007.060
Publisher: Springer Science and Business Media LLC
Date: 23-12-2016
Publisher: Elsevier BV
Date: 09-2020
Publisher: Wiley
Date: 25-08-2010
DOI: 10.1112/JLMS/JDQ046
Publisher: Cambridge University Press (CUP)
Date: 25-10-2017
DOI: 10.1017/S1446788716000343
Abstract: This article began as a study of the structure of infinite permutation groups $G$ in which point stabilisers are finite and all infinite normal subgroups are transitive. That led to two variations. One is the generalisation in which point stabilisers are merely assumed to satisfy min- n , the minimal condition on normal subgroups. The groups $G$ are then of two kinds. Either they have a maximal finite normal subgroup, modulo which they have either one or two minimal nontrivial normal subgroups, or they have a regular normal subgroup $M$ which is a isible abelian $p$ -group of finite rank. In the latter case the point stabilisers are finite and act irreducibly on a $p$ -adic vector space associated with $M$ . This leads to our second variation, which is a study of the finite linear groups that can arise.
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Location: United Kingdom of Great Britain and Northern Ireland
Start Date: 2017
End Date: 2017
Funder: London Mathematical Society
View Funded ActivityStart Date: 2019
End Date: 2019
Funder: London Mathematical Society
View Funded ActivityStart Date: 2016
End Date: 2021
Funder: Simons Foundation
View Funded Activity