Sufficient conditions for the root-class residuality of certain generalized free products

Sokolov, E. V.; Tumanova, E. A.

doi:10.1134/s0037446616010134

Cited by 18 publications

(2 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Proposition 6.11. [22,Proposition 8] If C is a root class of groups consisting only of periodic groups and X is a π(C)-bounded nilpotent group, then every π(C) ′ -isolated subgroup of X is C-separable in this group.…”

Section: Proofs Of Theorems 1-4 and Corollaries 1-4mentioning

confidence: 99%

Root class residuality of HNN-extensions with central cyclic associated subgroups

Sokolov

Tumanova

2017

Math Notes

Self Cite

View full text Add to dashboard Cite

Suppose that G is a group, H and K are proper isomorphic central subgroups of G, and G is an HNN-extension of G with the associated subgroups H and K. We prove necessary and sufficient conditions for G to be residually a C-group, where C is a class of groups closed under taking subgroups, extensions, homomorphic images, and Cartesian products of the form y∈Y X y , where X, Y ∈ C and X y is an isomorphic copy of X for each y ∈ Y .

show abstract

Section: Proofs Of Theorems 1-4 and Corollaries 1-4mentioning

confidence: 99%

Root class residuality of HNN-extensions with central cyclic associated subgroups

Sokolov

Tumanova

2017

Math Notes

Self Cite

View full text Add to dashboard Cite

show abstract

“…The notion of a root class was introduced in [10] and allows one to prove many statements at once using the same reasoning. It turns out to be especially useful in studying the residual properties of free constructions of groups (see, e.g., [22][23][24][25][26][27][28][29][30][31]). If X is such a construction and C is a root class of groups, then the C-separability of some subgroups of X is quite often one of the necessary and/or sufficient conditions for X to be residually a C-group.…”

Section: Introductionmentioning

confidence: 99%

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

Sokolov¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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

show abstract

Generalized Direct Products of Groups and their Application to the Study of Residuality of Free Constructions of Groups

Sokolov

Tumanova

2020

Algebra Logic

View full text Add to dashboard Cite

Sufficient conditions for the root-class residuality of certain generalized free products

Cited by 18 publications

References 16 publications

Root class residuality of HNN-extensions with central cyclic associated subgroups

Root class residuality of HNN-extensions with central cyclic associated subgroups

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

Generalized Direct Products of Groups and their Application to the Study of Residuality of Free Constructions of Groups

Contact Info

Product

Resources

About