A problem of Stallings on the direct square of a free group
HTML articles powered by AMS MathViewer
- by Gilbert Baumslag PDF
- Proc. Amer. Math. Soc. 104 (1988), 1007-1009 Request permission
Abstract:
Let $F$ be a free group of finite rank; let $\Delta (F)$ denote the diagonal subgroup of $F \times F$, and let $A$ and $B$ be finitely presented subgroups of $F \times F$. It is shown that $A \cap \Delta (F)$ is finitely presented, that, if neither $A$ nor $B$ is free, then $A \cap B$ is finitely presented, and that there are examples where both $A$ and $B$ are free of finite rank such that $A \cap B$ is not finitely generated.References
- Gilbert Baumslag and James E. Roseblade, Subgroups of direct products of free groups, J. London Math. Soc. (2) 30 (1984), no. 1, 44–52. MR 760871, DOI 10.1112/jlms/s2-30.1.44
- S. M. Gersten, On fixed points of certain automorphisms of free groups, Proc. London Math. Soc. (3) 48 (1984), no. 1, 72–90. MR 721773, DOI 10.1112/plms/s3-48.1.72
- Richard Z. Goldstein and Edward C. Turner, Fixed subgroups of homomorphisms of free groups, Bull. London Math. Soc. 18 (1986), no. 5, 468–470. MR 847985, DOI 10.1112/blms/18.5.468
- A. G. Howson, On the intersection of finitely generated free groups, J. London Math. Soc. 29 (1954), 428–434. MR 65557, DOI 10.1112/jlms/s1-29.4.428
- John R. Stallings, Graphical theory of automorphisms of free groups, Combinatorial group theory and topology (Alta, Utah, 1984) Ann. of Math. Stud., vol. 111, Princeton Univ. Press, Princeton, NJ, 1987, pp. 79–105. MR 895610
Additional Information
- © Copyright 1988 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 104 (1988), 1007-1009
- MSC: Primary 20F32; Secondary 20E05
- DOI: https://doi.org/10.1090/S0002-9939-1988-0931723-8
- MathSciNet review: 931723