(2, 3)-Generated Groups with Small Element Orders Full article
| Journal |
Algebra and Logic
ISSN: 0002-5232 , E-ISSN: 1573-8302 |
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| Output data | Year: 2021, Volume: 60, Number: 3, Pages: 217-222 Pages count : 6 DOI: 10.1007/s10469-021-09644-w | ||||||
| Tags | (2, 3)-generated group; involution; locally finite group; OCn-group | ||||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Mathematical Center in Akademgorodok | 075-15-2019-1675 |
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’s question for n = 8 for (2, 3)-generated groups. © 2021, Springer Science+Business Media, LLC, part of Springer Nature.
Cite:
Yang N.
, Mamontov A.S.
(2, 3)-Generated Groups with Small Element Orders
Algebra and Logic. 2021. V.60. N3. P.217-222. DOI: 10.1007/s10469-021-09644-w WOS Scopus OpenAlex
(2, 3)-Generated Groups with Small Element Orders
Algebra and Logic. 2021. V.60. N3. P.217-222. DOI: 10.1007/s10469-021-09644-w WOS Scopus OpenAlex
Identifiers:
| Web of science: | WOS:000714533400001 |
| Scopus: | 2-s2.0-85118526554 |
| OpenAlex: | W3212590410 |
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