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

2000/09/15 by Bilal Khan, Khan, Bilal
Computer Science · Mathematics · #05C25 (Secondary) #20E05 (Primary) #Advanced Topology and Set Theory #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:05C25 #msc:20E05 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.math/0009152

14 pages, 4 figures

arxiv created 2000/09/15 · openalex publication_date 2000/09/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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