Geodesic
On subgroups of free Burnside groups of odd exponent $n\geqslant 1003$
Izvestiya. Mathematics , Tome 73 (2009) no. 5, pp. 861-892

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We prove that for any odd number $n\geqslant 1003$, every non-cyclic subgroup of the 2-generator free Burnside group of exponent $n$ contains a subgroup isomorphic to the free Burnside group of exponent $n$ and infinite rank. Various families of relatively free $n$-periodic subgroups are constructed in free periodic groups of odd exponent $n\ge 665$. For the same groups, we describe a monomorphism $\tau$ such that a word $A$ is an elementary period of rank $\alpha$ if and only if its image $\tau(A)$ is an elementary period of rank $\alpha+1$.
Keywords: free Burnside group, variety of periodic groups, group with cyclic subgroups, periodic word, reduced word. 
@article{IM2_2009_73_5_a0,
     author = {V. S. Atabekian},
     title = {On subgroups of free {Burnside} groups of odd exponent $n\geqslant 1003$},
     journal = {Izvestiya. Mathematics },
     pages = {861--892},
     publisher = {mathdoc},
     volume = {73},
     number = {5},
     year = {2009},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_2009_73_5_a0/}
}
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V. S. Atabekian. On subgroups of free Burnside groups of odd exponent $n\geqslant 1003$. Izvestiya. Mathematics , Tome 73 (2009) no. 5, pp. 861-892. http://geodesic.mathdoc.fr/item/IM2_2009_73_5_a0/