|
This article is cited in 3 scientific papers (total in 3 papers)
On a matrix representation of a free group
A. N. Zubkov Omsk State Pedagogical University
Abstract:
An analog of the well-known Sanov representation of a free non-Abelian group by matrices of size $\ge3$ is studied. Instead of transvections used in the Sanov representation, we use matrices with “filled” first (second, etc.) column, except for the intersection with the diagonal, and we have ones on the diagonal and zeros at the other places. The “filled” places are occupied by the same parameter $k$. It is proved that, for $k\ge5$, these matrices generate a free group.
Received: 31.07.1997
Citation:
A. N. Zubkov, “On a matrix representation of a free group”, Mat. Zametki, 64:6 (1998), 863–870; Math. Notes, 64:6 (1998), 745–752
Linking options:
https://www.mathnet.ru/eng/mzm1465https://doi.org/10.4213/mzm1465 https://www.mathnet.ru/eng/mzm/v64/i6/p863
|
Statistics & downloads: |
Abstract page: | 498 | Full-text PDF : | 249 | References: | 61 | First page: | 1 |
|