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Journal of Siberian Federal University. Mathematics & Physics, 2023, Volume 16, Issue 4, Pages 413–419
(Mi jsfu1090)
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On generation of the groups $GL_n(\mathbb{Z})$ and $PGL_n(\mathbb{Z})$ by three involutions, two of which commute
Irina A. Markovskaya, Yakov N. Nuzhin Siberian Federal University, Krasnoyarsk, Russian Federation
Abstract:
It is proved that the general linear group $GL_n(\mathbb{Z})$ (its projective image $PGL_n(\mathbb{Z})$ respectively) over the ring of integers $\mathbb{Z}$ is generated by three involutions, two of which commute, if and only if $n\geqslant 5$ (if $n=2$ and $n \geqslant 5$ respectively).
Keywords:
general linear group, ring of integers, generating triples of involutions.
Received: 10.11.2022 Received in revised form: 24.01.2023 Accepted: 20.04.2023
Citation:
Irina A. Markovskaya, Yakov N. Nuzhin, “On generation of the groups $GL_n(\mathbb{Z})$ and $PGL_n(\mathbb{Z})$ by three involutions, two of which commute”, J. Sib. Fed. Univ. Math. Phys., 16:4 (2023), 413–419
Linking options:
https://www.mathnet.ru/eng/jsfu1090 https://www.mathnet.ru/eng/jsfu/v16/i4/p413
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Abstract page: | 84 | Full-text PDF : | 42 | References: | 16 |
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