Geodesic
On Periodic Groups of Odd Period $n\ge1003$
Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 495-500

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In the paper, using the Adyan–Lysenok theorem claiming that, for any odd number $n\ge1003$, there is an infinite group each of whose proper subgroups is contained in a cyclic subgroup of order $n$, it is proved that the set of groups with this property has the cardinality of the continuum (for a given $n$). Further, it is proved that, for $m\ge k\ge2$ and for any odd $n\ge1003$, the $m$-generated free $n$-periodic group is residually both a group of the above type and a $k$-generated free $n$-periodic group, and it does not satisfy the ascending and descending chain conditions for normal subgroups either.
Keywords: periodic group, group of bounded period, variety of groups of a given exponent, Adyan–Lysenok theorem.
Mots-clés : simple group 
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     author = {V. S. Atabekyan},
     title = {On {Periodic} {Groups} of {Odd} {Period} $n\ge1003$},
     journal = {Matemati\v{c}eskie zametki},
     pages = {495--500},
     publisher = {mathdoc},
     volume = {82},
     number = {4},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a1/}
}
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V. S. Atabekyan. On Periodic Groups of Odd Period $n\ge1003$. Matematičeskie zametki, Tome 82 (2007) no. 4, pp. 495-500. http://geodesic.mathdoc.fr/item/MZM_2007_82_4_a1/