2012/02/27 by Rostislav Grigorchuk, Grigorchuk, Rostislav · 3 citations
Mathematics · #Advanced Operator Algebra Research #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR
paper · pdf · doi:10.48550/arxiv.1202.6044
arXiv admin note: text overlap with arXiv:1111.0512
openalex publication_date 2012/02/27 · arxiv created 2012/09/18 · arxiv updated 2012/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We discuss some new results concerning Gap Conjecture on group growth and present a reduction of it (and its *-version) to several special classes of groups. Namely we show that its validity for the classes of simple groups and residually finite groups will imply the Gap Conjecture in full generality. A similar type reduction holds if the Conjecture is valid for residually polycyclic groups and just-infinite groups. The cases of residually solvable groups and right orderable groups are considered as well.