Abstract
The following theorem is proven. LetM be a closed, orientable, irreducible 3-manifold such that rankH 1(M, ℤ/pℤ)≥3 for some primep. Then either π1(M) is virtually solvable or it contains a free group of rank 2.
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Parry, W. A sharper tits alternative for 3-manifold groups. Israel J. Math. 77, 265–271 (1992). https://doi.org/10.1007/BF02773691
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DOI: https://doi.org/10.1007/BF02773691