(2, 3)-Generated Groups with Small Element Orders

Standard

(2, 3)-Generated Groups with Small Element Orders. / Yang, N.; Mamontov, A. S.

In: Algebra and Logic, Vol. 60, No. 3, 07.2021, p. 217-222.

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

Harvard

Yang, N & Mamontov, AS 2021, '(2, 3)-Generated Groups with Small Element Orders', Algebra and Logic, vol. 60, no. 3, pp. 217-222. https://doi.org/10.1007/s10469-021-09644-w

APA

Yang, N., & Mamontov, A. S. (2021). (2, 3)-Generated Groups with Small Element Orders. Algebra and Logic, 60(3), 217-222. https://doi.org/10.1007/s10469-021-09644-w

Vancouver

Yang N, Mamontov AS. (2, 3)-Generated Groups with Small Element Orders. Algebra and Logic. 2021 Jul;60(3):217-222. doi: 10.1007/s10469-021-09644-w

Author

Yang, N. ; Mamontov, A. S. / (2, 3)-Generated Groups with Small Element Orders. In: Algebra and Logic. 2021 ; Vol. 60, No. 3. pp. 217-222.

BibTeX

@article{44066514fb2b4622a9741bedd3d8b164,

title = "(2, 3)-Generated Groups with Small Element Orders",

abstract = "A periodic group is called an OCn-group if the set of its element orders consists of all natural numbers from 1 to some natural n. W. Shi posed the question whether every OCn-group is locally finite. Until now, the case n = 8 remains open. Here we prove that if a group is generated by an involution and an element of order 3, and its element orders do not exceed 8, then it is finite. Thereby we obtain an affirmative answer to Shi{\textquoteright}s question for n = 8 for (2, 3)-generated groups.",

keywords = "(2, 3)-generated group, involution, locally finite group, OC-group, OCn-group",

author = "N. Yang and Mamontov, {A. S.}",

note = "Funding Information: Supported by NNSF of China, grant No. 11301227. Publisher Copyright: {\textcopyright} 2021, Springer Science+Business Media, LLC, part of Springer Nature.",

year = "2021",

month = jul,

doi = "10.1007/s10469-021-09644-w",

language = "English",

volume = "60",

pages = "217--222",

journal = "Algebra and Logic",

issn = "0002-5232",

publisher = "Springer US",

number = "3",

}

RIS

TY - JOUR

T1 - (2, 3)-Generated Groups with Small Element Orders

AU - Yang, N.

AU - Mamontov, A. S.

PY - 2021/7

Y1 - 2021/7

N2 - A periodic group is called an OCn-group if the set of its element orders consists of all natural numbers from 1 to some natural n. W. Shi posed the question whether every OCn-group is locally finite. Until now, the case n = 8 remains open. Here we prove that if a group is generated by an involution and an element of order 3, and its element orders do not exceed 8, then it is finite. Thereby we obtain an affirmative answer to Shi’s question for n = 8 for (2, 3)-generated groups.

AB - A periodic group is called an OCn-group if the set of its element orders consists of all natural numbers from 1 to some natural n. W. Shi posed the question whether every OCn-group is locally finite. Until now, the case n = 8 remains open. Here we prove that if a group is generated by an involution and an element of order 3, and its element orders do not exceed 8, then it is finite. Thereby we obtain an affirmative answer to Shi’s question for n = 8 for (2, 3)-generated groups.

KW - (2, 3)-generated group

KW - involution

KW - locally finite group

KW - OC-group

KW - OCn-group

UR - http://www.scopus.com/inward/record.url?scp=85118526554&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/c575737f-5942-3d06-94ad-a53ce206429f/

U2 - 10.1007/s10469-021-09644-w

DO - 10.1007/s10469-021-09644-w

M3 - Article

AN - SCOPUS:85118526554

VL - 60

SP - 217

EP - 222

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 3

ER -

ID: 34599255