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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2011, Volume 17, Number 4, Pages 176–180
(Mi timm762)
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This article is cited in 1 scientific paper (total in 1 paper)
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.
Received: 16.08.2010
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
Linking options:
https://www.mathnet.ru/eng/timm762 https://www.mathnet.ru/eng/timm/v17/i4/p176
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Abstract page: | 247 | Full-text PDF : | 63 | References: | 31 | First page: | 5 |
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