Groups '93 Galway / St Andrews
Galway 1993
Volume 2
By C. M. Campbell
By E. F. Robertson
By T. C. Hurley
By S. J. Tobin
By J. J. Ward
Publisher: Cambridge University Press
Print Publication Year: 1995
Online Publication Date:February 2010
Online ISBN:9780511629297
Paperback ISBN:9780521477505
Chapter DOI: http://dx.doi.org/10.1017/CBO9780511629297.011
Subjects: Algebra
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Introduction
The study of infinite graphs has many aspects and various connections with other fields. There are the classical graph theoretic problems in infinite settings (see the survey by Thomassen [49]); there are special graph theoretical questions which have no direct analogues for finite graphs, such as questions about ends (see [7], [44] and the monograph [6]); Ramsey graph theory with its connections to set theory; the study of spectra of infinite graphs and random walks on infinite graphs (see the surveys [32] and [58]); the study of group actions on infinite graphs.
This survey is on the last subject, or rather on a small corner of the last subject. As is usual one concentrates on the case where the automorphism group acts transitively on the graph. The study of group actions can then be spilt up into three cases according to whether the graph under investigation has one, two or infinitely many ends. A graph has one end if there is always just one infinite component when finitely many vertices are removed from the graph. (“Component” will always mean a connected component in the graph theoretical sense.) The case of graphs with only one end is the hardest one, but in the special case of graphs with polynomial growth there are some very nice results (see [23]). The two ended case is the easiest one: roughly speaking these graphs all look like fat lines and one can say that they are very well understood (see [29] and [22]). Then there is the infinitely ended case, which is the one that this paper is all about.
pp. i-iv
pp. v-viii
pp. ix-x
pp. xi-xii
An army of cohomology against residual finiteness : Read PDF
pp. 305-313
On some questions concerning subnormally monomial groups : Read PDF
pp. 314-321
A conjecture concerning the evaluation of products of class-sums of the symmetric group : Read PDF
pp. 322-332
Automorphisms of Burnside rings : Read PDF
pp. 333-351
On finite generation of unit groups for group rings : Read PDF
pp. 352-367
Counting finite index subgroups : Read PDF
pp. 368-404
The quantum double of a finite group and its role in conformal field theory : Read PDF
pp. 405-417
Closure properties of supersoluble Fitting classes : Read PDF
pp. 418-425
Groups acting on locally finite graphs - a survey of the infinitely ended case : Read PDF
pp. 426-456
An invitation to computational group theory : Read PDF
pp. 457-475
On subgroups, transversals and commutators : Read PDF
pp. 476-481
Intervals in subgroup lattices of finite groups : Read PDF
pp. 482-494
Amalgams of minimal local subgroups and sporadic simple groups : Read PDF
pp. 495-506
Vanishing orbit sums in group algebras of p-groups : Read PDF
pp. 507-511
From stable equivalences to Rickard equivalences for blocks with cyclic defect : Read PDF
pp. 512-523
Factorizations in which the factors have relatively prime orders : Read PDF
pp. 524-527
Some problems and results in the theory of pro-p groups : Read PDF
pp. 528-542
On equations in finite groups and invariants of subgroups : Read PDF
pp. 543-548
Group presentations where the relators are proper powers : Read PDF
pp. 549-560
A condensing theorem : Read PDF
pp. 561-566
Lie methods in group theory : Read PDF
pp. 567-585
Some new results on arithmetical problems in the theory of finite groups : Read PDF
pp. 586-593
Groups that admit partial power automorphisms : Read PDF
pp. 594-601
pp. 602-609