ONE-RELATOR QUOTIENTS OF GRAPH PRODUCTS
نویسندگان
چکیده
منابع مشابه
One-Relator Quotients of Graph Products
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.
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It is proven that the Freiheitssatz holds for all one-relator products of cyclic groups if the relator is cyclically reduced and a proper power. The method of proof involves representing such groups in PSL2(C) and is a refinement of a technique of Baumslag, Morgan and Shalen. The technique allows the extension of the Freiheitssatz result to many additional one-relator products.
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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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We investigate the modular group as a finitely presented group. It has a large collection of interesting quotients. In 1987 Conder substantially identified the onerelator quotients of the modular group which are defined using representatives of the 300 inequivalent extra relators with length up to 24. We study all such quotients where the extra relator has length up to 36. Up to equivalence, th...
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Exponential equations in free groups were studied initially by Lyndon and Schützenberger [26] and then by Comerford and Edmunds [5]. Comerford and Edmunds showed that the problem of determining whether or not the class of quadratic exponential equations have solution is decidable, in finitely generated free groups. In this paper we show that for finite systems of quadratic exponential equations...
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ژورنال
عنوان ژورنال: International Journal of Algebra and Computation
سال: 2013
ISSN: 0218-1967,1793-6500
DOI: 10.1142/s0218196713500239