The structure of one-relator relative presentations and their centres
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...
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15 صفحه اولOn 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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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2009
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2009.024