Geodesic
$(2,3)$-generated groups with small element orders
Algebra i logika, Tome 60 (2021) no. 3, pp. 327-334

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A periodic group is called an $OC_n$-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 $OC_n$-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 subgroups.
Keywords: locally finite group, $(2,3)$-generated group, involution.
Mots-clés : $OC_n$-group 
@article{AL_2021_60_3_a5,
     author = {N. Yang and A. S. Mamontov},
     title = {$(2,3)$-generated groups with small element orders},
     journal = {Algebra i logika},
     pages = {327--334},
     publisher = {mathdoc},
     volume = {60},
     number = {3},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2021_60_3_a5/}
}
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N. Yang; A. S. Mamontov. $(2,3)$-generated groups with small element orders. Algebra i logika, Tome 60 (2021) no. 3, pp. 327-334. http://geodesic.mathdoc.fr/item/AL_2021_60_3_a5/