On weaker forms of relator Menger, relator Rothberger and relator Hurewicz properties
نویسندگان
چکیده
منابع مشابه
On One-relator Inverse Monoids and One-relator Groups
It is known that the word problem for one-relator groups and for one-relator monoids of the form Mon〈A ‖ w = 1〉 is decidable. However, the question of decidability of the word problem for general one-relation monoids of the form M = Mon〈A ‖ u = v〉 where u and v are arbitrary (positive) words in A remains open. The present paper is concerned with one-relator inverse monoids with a presentation o...
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It is a well-known fact that every group G has a presentation of the form G = F/R, where F is a free group and R the kernel of the natural epimorphism from F onto G. Driven by the desire to obtain a similar presentation of the group of automorphisms Aut(G), we can consider the subgroup Stab(R) ⊆ Aut(F ) of those automorphisms of F that stabilize R, and try to figure out if the natural homomorph...
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A recent result of D. J. Collins states that the intersection of two Magnus subgroups in a one-relator group consists either just of the ‘obvious’ intersection, or exceptionally of the free product of the obvious intersection with a free group of rank 1. In this paper, Collins’ result is generalised to apply to one-relator products of arbitrary locally-indicable groups. Moreover, a precise anal...
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In this paper, we generalise Magnus’ Freiheitssatz and solution to the word problem for one-relator groups by considering one relator quotients of certain classes of right-angled Artin groups and graph products of locally indicable polycyclic groups.
متن کاملSome results on one-relator surface groups
If S is noncompact, or has nonempty boundary, then π1(S) is free, and the answer to Question 1 is yes, by an old result of Magnus [7] on one-relator groups. (Essentially, the defining relator in a one-relator group on a given generating set is unique up to conjugacy and inversion.) We will show (see Theorem 3.4 below) that Question 1 also has an affirmative answer in the case of a closed surfac...
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ژورنال
عنوان ژورنال: Filomat
سال: 2012
ISSN: 0354-5180,2406-0933
DOI: 10.2298/fil1203427k