$ SQ$-universality of one-relator relative presentations
نویسندگان
چکیده
منابع مشابه
Udc 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 کاملUdc 512.543.7+512.543.16 Free Subgroups of One-relator Relative Presentations
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 کاملThe 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...
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 کاملAutomorphisms of One-relator Groups
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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ژورنال
عنوان ژورنال: Sbornik: Mathematics
سال: 2006
ISSN: 1064-5616,1468-4802
DOI: 10.1070/sm2006v197n10abeh003809