Geodesic
On a~subgroup of the Burnside group $B_0(2,5)$
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 176-180

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Let $x,y$ be generators of the universal 2-generated finite group of exponent $5$ (the $B_0(2,5)$-group). The structure of its subgroup $G=\langle xy,yx\rangle$ is investigated. It is shown that $|G|=5^{14}$ and the nilpotency class and derived length of $G$ are equal to $6$ and $3$, respectively. The lower and upper central series of $G$ are constructed. It is shown that $G$ is the largest 2-generated group of exponent $5$ and nilpotency class $6$.
Keywords: Burnside problem
Mots-clés : $B_0(2,5)$-group. 
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     author = {A. A. Kuznetsov},
     title = {On a~subgroup of the {Burnside} group $B_0(2,5)$},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {176--180},
     publisher = {mathdoc},
     volume = {17},
     number = {4},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a17/}
}
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A. A. Kuznetsov. On a~subgroup of the Burnside group $B_0(2,5)$. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 17 (2011) no. 4, pp. 176-180. http://geodesic.mathdoc.fr/item/TIMM_2011_17_4_a17/