On a matrix representation of a free group

A. N. Zubkov

Research output: Contribution to journalArticlepeer-review

Abstract

An analog of the well-known Sanov representation of a free non-Abelian group by matrices of size ≥ 3 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|≥ 5, these matrices generate a free group. However, for k = 2, this is not the case.

Original languageEnglish
Pages (from-to)745-752
Number of pages8
JournalMathematical Notes
Volume64
Issue number6
DOIs
Publication statusPublished - 1998
Externally publishedYes

Keywords

  • Congruence subgroup
  • Free group
  • Principal congruence subgroup
  • Sanov representation
  • Transvection

ASJC Scopus subject areas

  • General Mathematics

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