Subgroups of direct products of elementarily free groups
We exploit Zlil Sela's description of the structure of groups having the same elementary theory as free groups: they and their finitely generated subgroups form a prescribed subclass E of the hyperbolic limit groups. We prove that if $G_1,...,G_n$ are in E then a subgroup $\Gamma\subset G_1\t...
| প্রধান লেখক: | , |
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| বিন্যাস: | Journal article |
| ভাষা: | English |
| প্রকাশিত: |
2005
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| সংক্ষিপ্ত: | We exploit Zlil Sela's description of the structure of groups having the same elementary theory as free groups: they and their finitely generated subgroups form a prescribed subclass E of the hyperbolic limit groups. We prove that if $G_1,...,G_n$ are in E then a subgroup $\Gamma\subset G_1\times...\times G_n$ is of type $\FP_n$ if and only if $\Gamma$ is itself, up to finite index, the direct product of at most $n$ groups from $\mathcal E$. This answers a question of Sela. |
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