摘要:

At first sight, the argument which F. P. Ramsey gave for (the infinite case of) his famous theorem from 1927, is hopelessly unconstructive. If suitably reformulated, the theorem is true intuitionistically as well as classically: we offer a proof which should convince both the classical and the intuitionistic reader.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.193

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.212

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

A permutation group is said to be quasiprimitive if each of its nontrivial normal subgroups is transitive. A structure theorem for finite quasiprimitive permutation groups is proved, along the lines of the O'Nan‐Scott Theorem for finite primitive permutation groups. It is shown that every finite, non‐bipartite, 2‐arc transitive graph is a cover of a quasiprimitive 2‐arc transitive graph. The structure theorem for quasiprimitive groups is used to investigate the structure of quasiprimitive 2‐arc transitive graphs, and a new construction is given for a family of such graphs.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.227

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.240

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.255

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We study further the class of universal locally finite (u.l.f.)m‐extensionsEof a countable groupGin which the centralizerCE(G) is countable. These were introduced in [8]:m⊂ AutG/InnGis the fixed l.f. group of outer automorphisms ofGrealized inEandE/Gis locally finite and has the ‘ω‐injective property’ with respect to finitem‐extensionsFofG, that is,F/GCp(G) ⊂mandF/Gis finite. Here we shall prove that for mostG, if |m| =N1andN1=2N0then there areN2non‐isomorphic u.l.f.m‐extensionsEofGwith |CE,(G)| =N0. We also complete the presentation of [8] by showing that every countably infinite l.f. groupLhas 2N0locally homogeneousactions (onU(A), the countable u.l.f. central extension of any countable periodic abelian groupA[6, 11]) which extend any given action ofLonAand such that no infinite subactions of any two of these locally homogeneous actions are equivalent. We also construct 2N0nonembeddable locally homogeneous actions of manyLonU(A) which have ∞‐ω‐equivalent actions onU(A) of power 2m0. Finally we produce 2N1complete u.l.f. groups each of which has 2N0inequivalent universal actions on the countable u.l.f. group. (Universal actions were introduced in [8, Theorem 8] and are a categorical type of locally homogeneous action; the method of obtaining complete u.l.f. groups is that of [4].)

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.269

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.285

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

In our paper [6] we exploited parallel behaviour of the Mathieu groupsM12andM24 which we described fully in [4, 5], to obtain presentations of those groups given implicitly in terms of certain highly symmetric generating sets. We made precise the concepts ofsymmetric generating set, symmetric presentationandprimitive presentation, and indicated how these ideas can be generalized to other groups. In the present work, which is a continuation of [6], we turn the process around andseekgroups which possess generating sets with certain specified symmetries. We shall find that the most straightforward ways of generalizing [6] immediately give rise to the two smallest Janko groupsJ1andJ2Moreover the permutation actions of minimal degree of these two groups, on 266 and 100 letters respectively, emerge naturally and we are readily able to write down our symmetric generators in these representations. All assertions made can be easily checked on a computer, and we are again heavily indebted to the CAYLEY package. That said the final developments ofJ1andJ2given here, and in the sequel to this paper, are entirely by hand and are complete in all detail.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.294

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Letf(z) =∑j−1∞aj/(z−zj)and∑j−1∞|aj|/|zj| <  ∞.Thenfcan be realized as the complex conjugate of the gradient of a logarithmic potential or, for integralaj, as the logarithmic derivative of a meromorphic function. We investigate conditions onajandzjthat guarantee thatfhas zeros. In the potential theoretic setting, this asks whether certain logarithmic potentials with discrete mass distribution have equilibrium points.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.309

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We study Bäcklund transformations for a Boussinesq‐ or nonlinear string‐type equation and explicitly construct solutions for the associated modified equations. Our main results involve Miura‐type transformations and a careful study of factorizations of associated third‐order linear differential expressions.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-47.2.321

出版商:Oxford University Press    

年代:2016

数据来源: WILEY