In this article, we investigate the relationship between the minimum number of proper subgroups of GL(n, q) whose union is the whole GL(n, q) and the maximum number of elements that pairwise generate GL(n, q). We show that the minimum number of proper subrings of M_n(q) whose union is the whole M_n(q) is exactly the maximum number of elements that pairwise generate M_n(q).
Sets of Elements that Pairwise Generate a Matrix Ring
CRESTANI, ELEONORA
2012
Abstract
In this article, we investigate the relationship between the minimum number of proper subgroups of GL(n, q) whose union is the whole GL(n, q) and the maximum number of elements that pairwise generate GL(n, q). We show that the minimum number of proper subrings of M_n(q) whose union is the whole M_n(q) is exactly the maximum number of elements that pairwise generate M_n(q).
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