Relative hyperbolicity and similar properties of one-generator one-relator relative presentations with powered unimodular relator
نویسندگان
چکیده
منابع مشابه
The Structure of One-relator Relative Presentations and Their Centres
Suppose that G is a nontrivial torsion-free group and w is a word in the alphabet G∪{x 1 , . . . , x ±1 n } such that the word w ′ ∈ F (x1, . . . , xn) obtained from w by erasing all letters belonging to G is not a proper power in the free group F (x1, . . . , xn). We show how to reduce the study of the relative presentation Ĝ = 〈G, x1, x2, . . . , xn w = 1〉 to the case n = 1. It turns out that...
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Note that the existence of free subgroups in G̃ for n > 3 follows immediately from the free subgroup theorem for one-relator groups. Thus, Theorem 1 is nontrivial only for n = 2. The most difficult case is n = 1. An important role in this situation is played by the exponent sum of the generator in the relator. A word w = ∏ git εi ∈ G ∗ 〈t〉∞ is called unimodular if ∑ εi = 1. If the exponent sum o...
متن کاملOn 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...
متن کاملUdc 512.543.7+512.543.16 the Sq-universality of One-relator Relative Presentations
Adding two generators and one arbitrary relator to a nontrivial torsion-free group, we always obtain an SQ-universal group. In the course of the proof of this theorem, we obtain some other results of independent interest. For instance, adding one generator and one relator in which the exponent sum of the additional generator is one to a free product of two nontrivial torsion-free groups, we als...
متن کاملOn the Residual Finiteness and Other Properties of (relative) One-relator Groups
A relative one-relator presentation has the form P = 〈x,H;R〉 where x is a set, H is a group, and R is a word on x±1 ∪H. We show that if the word on x±1 obtained from R by deleting all the terms from H has what we call the unique max-min property, then the group defined by P is residually finite if and only if H is residually finite (Theorem 1). We apply this to obtain new results concerning the...
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ژورنال
عنوان ژورنال: Journal of Pure and Applied Algebra
سال: 2012
ISSN: 0022-4049
DOI: 10.1016/j.jpaa.2011.06.020