On the separability of subgroups of nilpotent groups by root classes of groups

被引：3

作者：

Sokolov, Evgeny Victorovich ^{[1
]}

机构：

[1] Ivanovo State Univ, Ivanovo, Russia

来源：

JOURNAL OF GROUP THEORY | 2023年 / 26卷 / 04期

基金：

俄罗斯科学基金会;

关键词：

GENERALIZED FREE-PRODUCTS; CLASS RESIDUALITY; CYCLIC SUBGROUP; FINITENESS;

D O I：

10.1515/jgth-2022-0021

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Suppose that e is a class of groups consisting only of periodic groups and beta(e/0 is the set of prime numbers that do not divide the order of any element of a e-group. It is easy to see that if a subgroup Y of a group X is e-separable in this group, then it is beta(e/0-isolated in X. Let us say that X has the property e-Sep if all of its beta(e/0-isolated subgroups are r-separable. We find a condition that is sufficient for a nilpotent group N to have the property r-Sep providede is a root class. We also prove that if N is torsion-free, then the indicated condition is necessary for this group to have r-Sep.

引用

页码：751 / 777

页数：27

共 50 条

[1] Separability of subgroups of nilpotent groups in the class of finite π-groups
Sokolov, E. V.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2014, 55 (06) : 1126 - 1132
[2] Separability of subgroups of nilpotent groups in the class of finite π-groups
E. V. Sokolov
[J]. Siberian Mathematical Journal, 2014, 55 : 1126 - 1132
[3] Separability of the subgroups of residually nilpotent groups in the class of finite π-groups
E. V. Sokolov
[J]. Siberian Mathematical Journal, 2017, 58 : 169 - 175
[4] Separability of the subgroups of residually nilpotent groups in the class of finite π-groups
Sokolov, E. V.
[J]. SIBERIAN MATHEMATICAL JOURNAL, 2017, 58 (01) : 169 - 175
[5] On the conjugacy separability of some free constructions of groups by root classes of finite groups
E. V. Sokolov
[J]. Mathematical Notes, 2015, 97 : 779 - 790
[6] On the conjugacy separability of some free constructions of groups by root classes of finite groups
Sokolov, E. V.
[J]. MATHEMATICAL NOTES, 2015, 97 (5-6) : 779 - 790
[7] The number of conjugacy classes of noncyclic subgroups of finite nilpotent groups
Wei, Boyan
Chen, Yinan
Liang, Xingliang
[J]. JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024,
[8] Subgroup separability of graphs of nilpotent groups
Metaftsis, V
Raptis, E
[J]. JOURNAL OF GROUP THEORY, 2004, 7 (02) : 265 - 273
[9] Groups with many nilpotent subgroups
Kurdachenko, LA
Shumyatsky, P
Subbotin, IY
[J]. ALGEBRA COLLOQUIUM, 2001, 8 (02) : 129 - 143
[10] FUZZY SUBGROUPS OF NILPOTENT GROUPS
ASAAD, M
ABOUZAID, S
[J]. FUZZY SETS AND SYSTEMS, 1993, 60 (03) : 321 - 323

← 1 2 3 4 5 →