Abstract.
We simplify the Steinberg presentation of SLn(Fd), where n≥1 and Fd is any finite field with d elements. That presentation has the elementary matrices eij(r), with i,j∈{1,...,n}, i≠=j and r∈Fd, 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 eij(r) and relations (E1)–(E3). In particular, relations (E3) are considerably reduced.
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Received: March 16, 1998; in final form: November 3, 2000¶Published online: October 2, 2001
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Chiaselotti, G. Some presentations for the special linear groups on finite fields. Ann. Mat. Pura Appl. IV. Ser. 180, 359–372 (2001). https://doi.org/10.1007/s102310100016
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DOI: https://doi.org/10.1007/s102310100016