Large and symmetric: The Khukhro--Makarenko theorem on laws --- without laws
Group Theory
2014-12-12 v4 Combinatorics
Rings and Algebras
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.
Keywords
Cite
@article{arxiv.1309.0571,
title = {Large and symmetric: The Khukhro--Makarenko theorem on laws --- without laws},
author = {Anton A. Klyachko and Maria V. Milentyeva},
journal= {arXiv preprint arXiv:1309.0571},
year = {2014}
}
Comments
12 pages, 3 figures. A Russian version of this paper is at http://halgebra.math.msu.su/staff/klyachko/papers.htm . V4: misprints corrected