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A problem of Stallings on the direct square of a free group


Author: Gilbert Baumslag
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
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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 [Enhancements On Off] (What's this?)

  • [1] Gilbert Baumslag and James E. Roseblade, Subgroups of direct products of free groups, J. London Math. Soc. (2) 30 (1984), 44-52. MR 760871 (86d:20028)
  • [2] S. M. Gersten, On fixed points of certain automorphisms of free groups, Proc. London Math. Soc. 48 (1984), 72-90. MR 721773 (85k:20075a)
  • [3] Richard Z. Goldstein and Edward C. Turner, Fixed subgroups of homomorphisms of free groups, Bull. London Math. Soc. 18 (1986), 468-470. MR 847985 (87m:20096)
  • [4] A. G. Howson, On the intersection of finitely generated free groups, J. London Math. Soc. 29 (1954), 428-434. MR 0065557 (16:444c)
  • [5] John R. Stallings, Graphical theory of automorphisms of free groups, combinatorial group theory and topology Annals of Math. Studies (1987), 79-105. Princeton University Press. 1984. MR 895610 (88i:20043)

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DOI: https://doi.org/10.1090/S0002-9939-1988-0931723-8
Article copyright: © Copyright 1988 American Mathematical Society

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