Generating Sequences of the Two Dimensional Special Projective Linear Group over Fields of Prime Order, PSL(2, p)
نویسنده
چکیده
As an infinite family of simple groups, the two dimensional special projective linear groups PSL(2,p) are interesting algebraic objects. While the groups are well known in the sense that their subgroup lattice structure is completely determined, properties of their generating sequences are still not entirely understood. With recent developments in this direction, one can begin to completely answer questions associated with the properties of generating sequences of PSL(2,p). The culmination of this discussion is in a conjecture for the size of irredundant generating sequences of the maximal length. A related notion to generating sequences is that of the replacement property an attribute of groups that is analogous to the Steinitz Exchange Property for vector spaces. It will be shown that PSL(2,p) sometimes has this property, but does not have it in general.
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