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.
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页码：480 / 493
页数：14
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