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 Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 4, Pages 176–180 (Mi timm762)

On a subgroup of the Burnside group $B_0(2,5)$

A. A. Kuznetsov

Siberian State Aerospace University

Abstract: 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, $B_0(2,5)$-group.

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UDC: 512.54

Citation: A. A. Kuznetsov, “On a subgroup of the Burnside group $B_0(2,5)$”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 4, 2011, 176–180

Citation in format AMSBIB
\Bibitem{Kuz11} \by A.~A.~Kuznetsov \paper On a~subgroup of the Burnside group $B_0(2,5)$ \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2011 \vol 17 \issue 4 \pages 176--180 \mathnet{http://mi.mathnet.ru/timm762} \elib{http://elibrary.ru/item.asp?id=17870435}