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.
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Supported by NNSF of China, grant No. 11301227.
Supported byMathematical Center in Akademgorodok, Agreement with RFMinistry of Education and Science No. 075-15-2019-1675.
Translated from Algebra i Logika, Vol. 60, No. 3, pp. 327-334, May-June, 2021. Russian DOI: https://doi.org/10.33048/alglog.2021.60.306.
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Yang, N., Mamontov, A.S. (2, 3)-Generated Groups with Small Element Orders. Algebra Logic 60, 217–222 (2021). https://doi.org/10.1007/s10469-021-09644-w
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DOI: https://doi.org/10.1007/s10469-021-09644-w