We prove that in all the Alternating and Symmetric groups the Moebius number of each subgroup can be bounded polinomially in terms of its index and the number of subgroups with a given index n and non trivial Moebius number grows at most polynomially in n. This result is an important step in order to prove a conjecture of A.Mann on the absolute convergency of the probabilistic series associated to a positively finitely generated profinite group.
On subgroups with non-zero Mobius numbers in the alternating and symmetric groups
LUCCHINI, ANDREA
2010
Abstract
We prove that in all the Alternating and Symmetric groups the Moebius number of each subgroup can be bounded polinomially in terms of its index and the number of subgroups with a given index n and non trivial Moebius number grows at most polynomially in n. This result is an important step in order to prove a conjecture of A.Mann on the absolute convergency of the probabilistic series associated to a positively finitely generated profinite group.
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