Large and symmetric: The Khukhro--Makarenko theorem on laws --- without laws
arXiv:1309.0571 · doi:10.1016/j.jalgebra.2014.10.029
Abstract
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.
12 pages, 3 figures. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V4: misprints corrected