On p-separability of subgroups of free metabelian groups

被引：2
作者：
Bardakov, VG [1 ]
机构：
[1] Sobolev Inst Math, Novosibirsk 630090, Russia
来源：
ALGEBRA COLLOQUIUM | 2006年 / 13卷 / 02期
关键词：
free metabelian group; nilpotent group; isolated subgroup; p-separable subgroup; Magnus representation;
D O I：
10.1142/S1005386706000253
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We prove that very free metabelian non-cyclic group has a finitely generated isolated subgroup which is not separable in the class of nilpotent groups. As a corollary, we prove that for every prime number p, an arbitrary free metabelian non-cyclic group has a finitely generated p'-isolated subgroup which is not p-separable.
引用
收藏
页码：289 / 294
页数：6
相关论文
共 9 条
[1]   AUTOMORPHISMS OF FREE METABELIAN GROUPS [J].
BACHMUTH, S .
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1965, 118 (06) :93-&
[2]   On D. I.!Moldavanskii's question about p-separable subgroups of a free group [J].
Bardakov, VG .
SIBERIAN MATHEMATICAL JOURNAL, 2004, 45 (03) :416-419
[3]  
Kargapolov MI, 1979, FUNDAMENTALS THEORY
[4]  
Loginova E. D., 1999, SIB MAT ZH, V40, p[341, 395]
[5]  
Lyndon R. C., 1977, Combinatorial group theory, V89
[6]  
Malcev, 1958, UCHEN ZAP IVANOVSKOG, V119, P49
[7]  
MALCEV A, 1976, SELECTED PAPERS, V1, P450
[8]  
NEUMANN H, 1967, ERGEBNISSE MATH IHRE, V37
[9]  
2002, KOUROVKA NOTEBOOK
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