The main result of this paper is a graph-theoretic necessary and sufficient condition, for a given set of transvections in SL (n, K) (n > 2 and K a finite field of characteristic not 2 or 3), to generate a group isomorphic to SL(m, L), for some m and some subfield L of K.
DI MARTINO, L., Previtali, A., Radina, R. (2005). Sets of transvections generating subgroups isomorphic to special linear groups. COMMUNICATIONS IN ALGEBRA, 33(6), 1663-1691 [10.1081/AGB-200058379].
Sets of transvections generating subgroups isomorphic to special linear groups
DI MARTINO, LINO GIUSEPPE;PREVITALI, ANDREA;
2005
Abstract
The main result of this paper is a graph-theoretic necessary and sufficient condition, for a given set of transvections in SL (n, K) (n > 2 and K a finite field of characteristic not 2 or 3), to generate a group isomorphic to SL(m, L), for some m and some subfield L of K.
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