Finite Subgroups of the Relatively Free $$\boldsymbol{n}$$-Torsion Groups

Autor: G. G. Gevorgyan, A. L. Gevorgyan
Rok vydání: 2020
Předmět:
Zdroj: Journal of Contemporary Mathematical Analysis (Armenian Academy of Sciences). 55:1-4
ISSN: 1934-9416
1068-3623
DOI: 10.3103/s1068362320010045
Popis: A group is called an $$n$$-torsion group if it has a system of defining relations of the form $$r^{n}=1$$ for some elements $$r$$, and for any of its finite order element $$a$$ the defining relation $$a^{n}=1$$ holds. In this paper, we prove that all the finite subgroups of the relatively free $$n$$-torsion groups are cyclic groups. Notice that for each rank $$m>1$$ and for any odd $$n\geq 1003$$, the set of nonisomorphic relatively free $$n$$-torsion groups of rank $$m$$ has the cardinality of the continuum.
Databáze: OpenAIRE
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