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Generalized Rigid Groups : Definitions, Basic Properties, and Problems. / Romanovskii, N. S.

In: Siberian Mathematical Journal, Vol. 59, No. 4, 01.07.2018, p. 705-709.

Research output: Contribution to journal › Article › peer-review

Harvard

Romanovskii, NS 2018, 'Generalized Rigid Groups: Definitions, Basic Properties, and Problems', Siberian Mathematical Journal, vol. 59, no. 4, pp. 705-709. https://doi.org/10.1134/S0037446618040122

APA

Romanovskii, N. S. (2018). Generalized Rigid Groups: Definitions, Basic Properties, and Problems. Siberian Mathematical Journal, 59(4), 705-709. https://doi.org/10.1134/S0037446618040122

Vancouver

Romanovskii NS. Generalized Rigid Groups: Definitions, Basic Properties, and Problems. Siberian Mathematical Journal. 2018 Jul 1;59(4):705-709. doi: 10.1134/S0037446618040122

Author

Romanovskii, N. S. / Generalized Rigid Groups : Definitions, Basic Properties, and Problems. In: Siberian Mathematical Journal. 2018 ; Vol. 59, No. 4. pp. 705-709.

BibTeX

@article{5a94d9b9d43f4afeb7de09085d83b874,

title = "Generalized Rigid Groups: Definitions, Basic Properties, and Problems",

abstract = "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.",

keywords = "divisible group, group axioms, soluble group, SOLUBLE GROUPS",

author = "Romanovskii, {N. S.}",

note = "Publisher Copyright: {\textcopyright} 2018, Pleiades Publishing, Ltd.",

year = "2018",

month = jul,

day = "1",

doi = "10.1134/S0037446618040122",

language = "English",

volume = "59",

pages = "705--709",

journal = "Siberian Mathematical Journal",

issn = "0037-4466",

publisher = "MAIK NAUKA/INTERPERIODICA/SPRINGER",

number = "4",

}

RIS

TY - JOUR

T1 - Generalized Rigid Groups

T2 - Definitions, Basic Properties, and Problems

AU - Romanovskii, N. S.

PY - 2018/7/1

Y1 - 2018/7/1

N2 - 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.

AB - 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.

KW - divisible group

KW - group axioms

KW - soluble group

KW - SOLUBLE GROUPS

UR - http://www.scopus.com/inward/record.url?scp=85052996130&partnerID=8YFLogxK

U2 - 10.1134/S0037446618040122

DO - 10.1134/S0037446618040122

M3 - Article

AN - SCOPUS:85052996130

VL - 59

SP - 705

EP - 709

JO - Siberian Mathematical Journal

JF - Siberian Mathematical Journal

SN - 0037-4466

IS - 4

ER -

ID: 16485634