On the residual finiteness and other properties of (relative) one-relator groups

Details On the residual finiteness and other properties of (relative) one-relator groups On the residual finiteness and other properties of (relative) one-relator groups

2007-06-22

arxiv.org/abs/0706.3338v1

Mathematics

Group Theory

Scientific paper

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 group word on X and H. We show that if the group word on X 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 residual finiteness of (ordinary) one-relator groups (Theorem 4). We also obtain results concerning the conjugacy problem for one-relator groups (Theorem 5), and results concerning the relative asphericity of presentations of the form P (Theorem 6).

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