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

#### 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 reduced
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Presentations of groups; Linear Special Groups; Elementary Matrices
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11770/158490
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