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

Baumslag, Gilbert

doi:10.1090/S0002-9939-1988-0931723-8

A problem of Stallings on the direct square of a free group
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by Gilbert Baumslag

Proc. Amer. Math. Soc. 104 (1988), 1007-1009

DOI: https://doi.org/10.1090/S0002-9939-1988-0931723-8

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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

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