2013/09/30 by Anton A. Klyachko, Maria V. Milentyeva · 1 citation
Mathematics · #Combinatorics #Corollary #Dual (grammatical number) #Finite Group Theory Research #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology #Identity (music) #Law #Mathematics #Multilinear map #Philosophy #Planarity testing #Pure mathematics #math.CO #math.GR #math.RA
paper · pdf · doi:10.1016/j.jalgebra.2014.10.029
published as Journal of Algebra, 2015, 424, 222-241 · 12 pages, 3 figures. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V4: misprints corrected
arxiv created 2014/10/26 · openalex publication_date 2014/12/11 · arxiv updated 2014/12/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We prove a generalisation of the Khukhro--Makarenko theorem on large characteristic subgroups with laws. This general fact implies new results on groups, algebras, and even graphs and other structures. Concerning groups, we obtain, e.g., a fact in a sense dual to the Khukhro--Makarenko theorem. A graph-theoretic corollary is an analogue of this theorem in which planarity plays the role of a multilinear identity. We answer also a question of Makarenko and Shumyatsky.