What is the largest possible size of a subset of SL(n, Z) from which every pair of elements will be a generating set? We prove a general result on generation probabilities in profinite groups that suggests the cardinality of a maximal such subset equals that of the analogous subset of SL(n, Z/2Z).
d-WISE GENERATION OF SOME INFINITE GROUPS
LUCCHINI, ANDREA;
2008
Abstract
What is the largest possible size of a subset of SL(n, Z) from which every pair of elements will be a generating set? We prove a general result on generation probabilities in profinite groups that suggests the cardinality of a maximal such subset equals that of the analogous subset of SL(n, Z/2Z).
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