Approximation by Subgroups of Finite Index and the Hanna Neumann Conjecture
نویسندگان
چکیده
Let F be a free group (pro-p group) and U and W two finitely generated subgroups (closed subgroups) of F . The Strengthened Hanna Neumann conjecture says that ∑ x∈U\F/W rk(U ∩ xWx−1) ≤ rk(U)rk(W ), where rk(U) = max{rk(U)− 1, 0}. This conjecture was proved in the case of abstract groups independently by J. Friedman and I. Mineyev in 2011. In this paper we give the proof of the conjecture in the pro-p context and also present a new proof in the abstract case. We also show that the Lück approximation conjecture holds for free groups.
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