The Hanna Neumann Conjecture is true when one subgroup has a positive generating set

Details The Hanna Neumann Conjecture is true when one subgroup has a positive generating set The Hanna Neumann Conjecture is true when one subgroup has a positive generating set

2000-09-15

arxiv.org/abs/math/0009152v1

Mathematics

Group Theory

14 pages, 4 figures

Scientific paper

The Hanna Neumann conjecture states that if F is a free group, then for all finitely generated subgroups H,K <= F, rank(H intersect K) - 1 <= [ 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 <= F({a,b}) is part of a counterexample to the conjecture, then its folding Gamma_H must contain source and/or sink vertices.

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