The residual finiteness of certain one-relator groups

Allenby, R. B. J. T.; Moser, L. E.; Tang, C. Y.

doi:10.1090/S0002-9939-1980-0548072-5

The residual finiteness of certain one-relator groups
HTML articles powered by AMS MathViewer

by R. B. J. T. Allenby, L. E. Moser and C. Y. Tang

Proc. Amer. Math. Soc. 78 (1980), 8-10

DOI: https://doi.org/10.1090/S0002-9939-1980-0548072-5

PDF | Request permission

Abstract:

We prove that the groups $\langle a,b;{({a^{ - 1}}{b^l}a{b^m})^t}\rangle$, where $l,m,t \in Z$ and $t \geqslant 2$ are residually finite ${(_R}F)$, thus establishing a conjecture of G. Baumslag [Bull. Amer. Math. Soc. 73 (1967), 618-620].

References

Benjamin Baumslag and Marvin Tretkoff, Residually finite HNN extensions, Comm. Algebra 6 (1978), no. 2, 179–194. MR 484178, DOI 10.1080/00927877808822240
Gilbert Baumslag, Residually finite one-relator groups, Bull. Amer. Math. Soc. 73 (1967), 618–620. MR 212078, DOI 10.1090/S0002-9904-1967-11799-3
Gilbert Baumslag, On the residual finiteness of generalised free products of nilpotent groups, Trans. Amer. Math. Soc. 106 (1963), 193–209. MR 144949, DOI 10.1090/S0002-9947-1963-0144949-8
Gilbert Baumslag, On generalised free products, Math. Z. 78 (1962), 423–438. MR 140562, DOI 10.1007/BF01195185
R. G. Burns, On finitely generated subgroups of free products, J. Austral. Math. Soc. 12 (1971), 358–364. MR 0311778