GENERALIZED DIRECT PRODUCTS OF GROUPS AND THEIR APPLICATION TO THE STUDY OF RESIDUALITY OF FREE CONSTRUCTIONS OF GROUPS

被引：9

作者：

Sokolov, E. V. ^{[1
]}

Tumanova, E. A. ^{[1
]}

机构：

[1] Ivanovo State Univ, Ul Ermaka 39, Ivanovo 153025, Russia

来源：

ALGEBRA AND LOGIC | 2020年 / 58卷 / 06期

关键词：

generalized direct product; generalized free product; HNN-extension; residual finiteness; residual p-finiteness; residual solvability; root-class residuality; ROOT-CLASS RESIDUALITY; HNN-EXTENSIONS; SUBGROUPS;

D O I：

10.1007/s10469-020-09568-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the construction of a generalized direct product associated with a graph of groups and prove two sufficient conditions for its existence. These results are applied to obtain some sufficient conditions for an HNN-extension with central associated subgroups to be residually a C-group where C is a root class of groups. In particular, it is proved that an HNN-extension of a solvable group with central associated subgroups is residually solvable.

引用

页码：480 / 493

页数：14

共 28 条

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