Large and symmetric: The Khukhro-Makarenko theorem on laws - without laws

JOURNAL OF ALGEBRA

卷:424

Article

Klyachko, Anton A.¹  Milentyeva, Maria V.¹ 

[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119991, Russia

关键词: Khukhro-Makarenko theorem;    Automorphism invariance;    Groups;    Rings;    Graphs;    Planarity;   

DOI  :  10.1016/j.jalgebra.2014.10.029

来源: Elsevier

【 摘 要 】

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. Also, we answer a question of Makarenko and Shumyatsky. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free