ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.1

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We show that an arbitrary GCD domain can be embedded in a Bézout domain without changing the set of units. This result continues to hold if we require the domains to be discretely ordered. We can thus construct Bézout domains which are models of open induction and in which the order type of the set of positive infinite primes is arbitrary of cardinality ⩽ ℵ1.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.15

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

A ring is called weakly finite if all of its right invertible square matrices are invertible. Given a set of square matrices over a ring, there is the notion of the (universal) matrix localization with respect to that set, which adjoins a universal inverse for each matrix in the set. Under mild conditions on the set of matrices to be inverted (that it is a multiplicative factor‐closed set of full matrices), we show that such a matrix localization of any ring is weakly finite. Related results are also given.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.31

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Let δ(H) be the minimum degree of the graphH. We prove that a graphHof ordernwith δ(H) ⩾ (2n−1)/3 contains any graphGof order at mostnand maximum degree Δ(G) ⩽ 2 as a subgraph, and this bound is best possible. Furthermore, this result settles the case Δ(G) = 2 of the well‐known conjecture of Bollobás, Catlin and Eldridge on packing two graphs with given maximum degree.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.39

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We study the unification problem for the theories of nilpotent groups of class at least 5. This is equivalent to the problem of constructing an algorithm which will solve any equation in a free nilpotent group of class at least 5. Romankov in 1977 showed that the ‘endomorphic reducibility’ problem is undecidable for free nilpotent groups of class at least 9 and it follows that the Unification Problem for the theories of nilpotent groups of class at least 9 is undecidable. We shall improve this to 5 by reducing the problem of algorithmically solving an arbitrary diophantine equation of degree 4 to that of solving equations in a free nilpotent group of class 5 and then appealing to Matiyasevitch's Theorem.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.52

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.59

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

Higman has questioned which discrete hyperbolic groups [p, q] have representations onto almost all symmetric and alternating groups. We call this propertyhand show that, except perhaps for finitely many values ofpandq, [p, q] has propertyh.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.77

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

A class of covers of the free monogenic inverse monoid is introduced in one‐to‐one correspondence with the irrational numbers greater than one. Each member of the class is an eventually regular semigroup with a generatora, the regular powers of which form a pseudo‐random set. This then affords an example of a direct product of two eventually regular semigroups that is not eventually regular, thus answering a question of P. M. Edwards.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.87

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

A characterization is given of the weightsr, p, vwhen the weighted norm inequality(∫ab|rf|q)1/q⩽C(∫ab|pf′|q+∫ab|vf|p)1/pholds. Both cases 1 ⩽p⩽q⩽ ∞ and 1 ⩽q

ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.103

出版商:Oxford University Press    

年代:2016

数据来源: WILEY

摘要:

We show that the least genus of any compact Riemann surfaceS, admitting a simple Suzuki groupG= Sz(q) as a group of automorphisms, is equal to 1 + |G|/40. We compute the number of such surfacesSas the number of normal subgroups of the triangle group Δ(2,4,5) with quotient‐groupG, and investigate the associated regular maps of type {4, 5}.

ISSN:0024-6107    

DOI:10.1112/jlms/s2-48.1.117

出版商:Oxford University Press    

年代:2016

数据来源: WILEY