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We present a hypersurface singularity in positive characteristic which isdefined by a purely inseparable power series, and a sequence of point blowupsso that, after applying the blowups to the singularity, the same type ofsingularity reappears after the last blowup, with just certain exponents of thedefining power series shifted upwards. The construction hence yields a cycle.Iterating this cycle leads to an infinite increase of the residual order of thedefining power series. This disproves a theorem claimed by Moh about thestability of the residual order under sequences of blowups. It is not acounter-example to the resolution in positive characteristic since largercenters are also permissible and prevent the phenomenon from happening.

Cycles of Singularities appearing in the Resolution Problem in positive Characteristic