Generalized Rigid Groups: Definitions, Basic Properties, and Problems

Сибирский математический журнал

N. S. Romanovskii¹ 

[1] Novosibirsk State University

关键词: soluble group;    divisible group;    group axioms;   

DOI  :  10.1134/S0037446618040122

学科分类：数学（综合）

来源: Izdatel stvo Instituta Matematiki Rossiiskoi Akademii Nauk

【 摘 要 】

We find a natural generalization of the concept of rigid group. The generalized rigid groups are also called r-groups. The terms of the corresponding rigid series of every r-group can be characterized by both ∃-formulas and ∀-formulas. We find a recursive system of axioms for the class of r-groups of fixed solubility length. We define divisible r-groups and give an appropriate system of axioms. Several fundamental problems are stated.

【 授权许可】

CC BY