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Problemy Fiziki, Matematiki i Tekhniki (Problems of Physics, Mathematics and Technics), 2011, Issue 3(8), Pages 81–83
(Mi pfmt122)
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MATHEMATICS
The representation image unipotency of the group $F_2$ by mapping primitive elements into unipotent matrices with small Jordan blocks
O. I. Tavgen'a, D. Junhuab, L. Chunyan a Belarusian State University, Minsk
b College of Sciences of Qiqihar University, Qiqihar, China
Abstract:
It is proved that the representation image of the free group $F_2(x, y)$ in $GL(n, C))$ is an unipotent subgroup, when $(\rho (p) - E)^5 = 0$ for all primitive elements $p$ and $(\rho(\xi) - E)^2 = 0$, $(\rho(\gamma) - E)^3 = 0$ for some associated primitive elements $\xi$ and $\gamma$ of the group $F_2$ .
Keywords:
unipotent subgroup, primitive element, representation of group.
Received: 30.05.2011
Citation:
O. I. Tavgen', D. Junhua, L. Chunyan, “The representation image unipotency of the group $F_2$ by mapping primitive elements into unipotent matrices with small Jordan blocks”, PFMT, 2011, no. 3(8), 81–83
Linking options:
https://www.mathnet.ru/eng/pfmt122 https://www.mathnet.ru/eng/pfmt/y2011/i3/p81
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Abstract page: | 121 | Full-text PDF : | 74 | References: | 25 |
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