Recognizing \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ A_{7} $\end{document} by Its Set of Element Orders

被引：0
作者：
A. S. Mamontov
E. Jabara
机构：
[1] Sobolev Institute of Mathematics,Universitá di Ca’Foscari
[2] Dipartimento di Filosofia e Beni Culturali,undefined
来源：
Siberian Mathematical Journal | 2021年 / 62卷 / 1期
关键词：
periodic group; locally finite group; spectrum; 517.518.85;
D O I：
10.1134/S0037446621010109
中图分类号：
学科分类号：
摘要：
Let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ G $\end{document} be a periodic group, and let \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ \omega(G)\subseteq{𝕅} $\end{document} be the spectrum of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ G $\end{document} that is the set of orders of elements in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ G $\end{document}. We prove that the alternating group \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$ A_{7} $\end{document} is uniquely recognized by its spectrum in the class of all groups.
引用
收藏
页码：93 / 104
页数：11
相关论文
共 35 条
[1]  
Grechkoseeva MA(2015)On the structure of finite groups isospectral to finite simple groups J. Group Theory 18 741-759
[2]  
Vasil’ev AV(1999)On recognition of the finite simple groups Sib. Math. J. 40 62-64
[3]  
Zhurtov AK(2007) in the class of all groups Sib. Electronic Math. Reports 4 300-303
[4]  
Mazurov VD(2014)Recognizability by spectrum of the group Int. J. Algebra Comput. 24 113-119
[5]  
Lytkina DV(2015) in the class of all groups Algebra and Logic 54 279-282
[6]  
Kuznetsov AA(2015)Recognizing Algebra and Logic 54 161-166
[7]  
Jabara E(1991) by spectrum in the class of all groups J. Algebra 143 388-400
[8]  
Lytkina D(2020)Recognizing  Sib. Math. J. 61 109-117
[9]  
Mamontov A(2020) by the set of element orders in the class of all groups Sib. Math. J. 61 1093-1101
[10]  
Mamontov AS(1937)Infinite groups of finite period J. Lond. Math. Soc. s1–12 195-198
1234