Representing subalgebras as retracts of finite subdirect powers

被引：0
作者：
Keith A. Kearnes
Alexander Rasstrigin
机构：
[1] University of Colorado,Department of Mathematics
[2] Volgograd State Socio-Pedagogical University,Department of Higher Mathematics and Physics
来源：
Algebra universalis | 2020年 / 81卷
关键词：
Formation; Higher commutator; Nilpotent; Pseudovariety; Retract; Subalgebra; Subdirect power; Supernilpotent; Two term condition; 08A05; 08A30; 08A60; 20F17;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We prove that if A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {A}}$$\end{document} is an algebra that is supernilpotent with respect to the 2-term higher commutator, and B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {B}}$$\end{document} is a subalgebra of A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {A}}$$\end{document}, then B\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathbb {B}}$$\end{document} is representable as a retract of a finite subdirect power of A\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb A$$\end{document}.
引用
收藏
相关论文
共 12 条
[1]  
Aichinger E(2010)Some applications of higher commutators in Mal’cev algebras Algebra Univers. 63 367-403
[2]  
Mudrinski N(1999)Congruence modular varieties with small free spectra Algebra Univers. 42 165-181
[3]  
Kearnes KA(2010)An axiomatic formation that is not a variety J. Group Theory 13 233-241
[4]  
Kearnes Keith A(1998)The relationship between two commutators Int. J. Algebra Comput. 8 497-531
[5]  
Kearnes KA(2020)Is supernilpotence super nilpotence? Algebra Univers. 81 3-476
[6]  
Szendrei Á(1992)Three remarks on the modular commutator Algebra Univers. 29 455-158
[7]  
Kearnes KA(2018)Higher commutator theory for congruence modular varieties J. Algebra 513 133-90
[8]  
Szendrei Á(1970)A note on formations of finite nilpotent groups Bull. Lond. Math. Soc. 2 91-undefined
[9]  
Kiss EW(1970)Characteristic subgroups of free groups Bull. Lond. Math. Soc. 2 87-undefined
[10]  
Moorhead A(undefined)undefined undefined undefined undefined-undefined
12