A group with an infinite number of Nielsen inequivalent one-relator presentations
نویسندگان
چکیده
منابع مشابه
Udc 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...
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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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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1976
ISSN: 0021-8693
DOI: 10.1016/0021-8693(76)90027-2