Let L be a finite group with a unique minimal normal subgroup, say N. We study the conditional probability P_{L,N} (d) that d randomly chosen elements of L generate L given that they generated L modulo N. In particular we prove that if d ≥ d(L) then P_{L,N} (d) ≥ 1/2. Several applications to general questions on the generation of finite and profinite groups are described.
Probabilistic generation of finite groups with a unique minimal normal subgroup
DETOMI, ELOISA MICHELA;LUCCHINI, ANDREA
2013
Abstract
Let L be a finite group with a unique minimal normal subgroup, say N. We study the conditional probability P_{L,N} (d) that d randomly chosen elements of L generate L given that they generated L modulo N. In particular we prove that if d ≥ d(L) then P_{L,N} (d) ≥ 1/2. Several applications to general questions on the generation of finite and profinite groups are described.File in questo prodotto:
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