Abstract
IfV is a projectiveKH-module, whereK is a field of prime orderp andH is a finite group, then it is shown, thatV can be extended up to equivalence to a free pro-p groupP on whichH acts, such that the action ofH onV is equivalent to the induced action ofH on the Frattini factor group ofP. This can be used to show, that the action ofH on any finitep-group is induced from the action ofH on a suitable free pro-p group.
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Baumann, B. Free pro-p groups with operators. Manuscripta Math 73, 385–396 (1991). https://doi.org/10.1007/BF02567649
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DOI: https://doi.org/10.1007/BF02567649