We simplify the Steinberg presentation of $SL_n(F_d)$, where $n ≥ 1$ and $F_d$ is any finite field with $d$ elements. That presentation has the elementary matrices $e_{ij}(r)$, with $i, j \in \{1, . . . , n\},i=j$ and $r\in F_d$, as generators, and (E1)–(E3), described at the opening of this work, as relations. The presentation that we shall obtain reduces the number of generators $e_{ij}(r)$ and relations (E1)–(E3). In particular, relations (E3) are considerably reduced
Some presentations for the Special Linear Groups on Finite Fields
CHIASELOTTI, Giampiero
2001-01-01
Abstract
We simplify the Steinberg presentation of $SL_n(F_d)$, where $n ≥ 1$ and $F_d$ is any finite field with $d$ elements. That presentation has the elementary matrices $e_{ij}(r)$, with $i, j \in \{1, . . . , n\},i=j$ and $r\in F_d$, as generators, and (E1)–(E3), described at the opening of this work, as relations. The presentation that we shall obtain reduces the number of generators $e_{ij}(r)$ and relations (E1)–(E3). In particular, relations (E3) are considerably reducedFile in questo prodotto:
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