Reflections on the residual finiteness of one-relator groups
نویسندگان
چکیده
منابع مشابه
Reflections on the residual finiteness of one-relator groups
Let G D ha; b; : : : j r D 1i be a one-relator group equipped with at least two generators. For all w which do not commute with r in the ambient free group on the generators a, b, ..., the groups G.r;w/ D ha; b; : : : j rrw D r2i are not residually finite and have the same finite images as G. The existence of this family of one-relator groups which are not residually finite reinforces what is b...
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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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If S is noncompact, or has nonempty boundary, then π1(S) is free, and the answer to Question 1 is yes, by an old result of Magnus [7] on one-relator groups. (Essentially, the defining relator in a one-relator group on a given generating set is unique up to conjugacy and inversion.) We will show (see Theorem 3.4 below) that Question 1 also has an affirmative answer in the case of a closed surfac...
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ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2007
ISSN: 1661-7207
DOI: 10.4171/ggd/11