2009/07/13 by Ted Hurley, Hurley, Ted
Mathematics · #20E18 #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Rings and Algebras (math.RA) #math.GR #math.RA #msc:20E18
paper · pdf · doi:10.48550/arxiv.0907.2146
11 pages
arxiv created 2009/07/13 · openalex publication_date 2009/07/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Factors (X)/(Y) in a free group F with Y normal in X are considered. Precise results on the free structure of Y relative to the free structure of X when (X)/(Y) is abelian are obtained. Some extensions and applications are given, as for example to the construction of lower central factors in general groups. A collecting process on free generators, which gives basic commutator-type free generators for some subgroups, is also presented. The notion of \em relative basic commutators is developed.