Two-generator one-relator groups and marked polytopes
نویسندگان
چکیده
منابع مشابه
The Two - Generator Subgroups of One - Relator Groups with Torsion
The main aim of this paper is to show that every two-generator subgroup of any one-relator group with torsion is either a free product of cyclic groups or is a one-relator group with torsion. This result is proved by using techniques for reducing pairs of elements in certain HNN groups. These techniques not only apply to one-relator groups with torsion but also to a large number of other groups...
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The main result of this paper is a complete classification of the outer automorphism groups of two-generator, one-relator groups with torsion. To this classification we apply recent algorithmic results of Dahmani– Guirardel, which yields an algorithm to compute the isomorphism class of the outer automorphism group of a given two-generator, one-relator group with torsion.
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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...
متن کاملThe surjectivity problem for one-generator, one-relator extensions of torsion-free groups
We prove that the natural map G → Ĝ, where G is a torsionfree group and Ĝ is obtained by adding a new generator t and a new relator w , is surjective only if w is conjugate to gt where g ∈ G . This solves a special case of the surjectivity problem for group extensions, raised by Cohen [2]. AMS Classification 20E22, 20F05; 57M20, 57Q10
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ژورنال
عنوان ژورنال: Annales de l'Institut Fourier
سال: 2020
ISSN: 1777-5310
DOI: 10.5802/aif.3325