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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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/

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