Formal Statement
Let H, K ≤ F(X) be two nontrivial finitely generated subgroups of a free group F(X) and let L = H ∩ K be the intersection of H and K. The conjecture says that in this case
- rank(L) − 1 ≤ (rank(H) − 1)(rank(K) − 1).
Here for a group G the quantity rank(G) is the rank of G, that is, the smallest size of a generating set for G. Every subgroup of a free group is known to be free itself and the rank of a free group is equal to the size of any free basis of that free group.
Read more about this topic: Hanna Neumann Conjecture
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