The generation of the augmentation ideal in profinite groups
Tóm tắt
We find a formula for computing the minimum number of generators for the augmentation ideal in the profinite setting; this is a generalisation of a result obtained in the finite case by Cossey, Gruenberg and Kovács. We then consider probabilistic questions connected with the generation of the augmentation ideal and we define the class of APFG groups as those profinite groups for which the probability of generating the augmentation ideal with t random elements is non-zero for some t ∈ ℕ. We give a characterisation of these groups which allows us easily to compare APFG groups with PFG groups and we show that PFG groups are APFG but we give examples showing that this is a strict inclusion.
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