The Hanna Neumann Conjecture Is True When One Subgroup Has a Positive Generating Set
نویسنده
چکیده
The Hanna Neumann conjecture states that if F is a free group, then for all finitely generated subgroups H,K 6 F , rank(H ∩ K) − 1 6 [rank(H)− 1] [rank(K)− 1] In this paper, we show that if one of the subgroups, say H , has a generating set consisting of only positive words, then H is not part of any counterexample to the conjecture. We further show that if H ≤ F2 is part of a counterexample to the conjecture, then its folding ΓH must contain source and/or sink vertices.
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