  Nipotency of skew braces is related to certain types of solutions of the
Yang-Baxter equation. This paper delves into the study of centrally nilpotent
skew braces. In particular, we study their torsion theory (Section 4.1) and we
introduce an "index" for subbraces (Section 4.2), but we also show that the
product of centrally nilpotent ideals need not be centrally nilpotent (Example
B), a rather peculiar fact. To cope with these examples, we introduce a special
type of nilpotent ideal, using which, we define a {\it good} Fitting ideal.
Also, a Frattini ideal is defined and its relationship with the Fitting ideal
is investigated.
  A key ingredient in our work is the characterisation of the commutator of
ideals in terms of absorbing polynomials (Section 3); this solves Problem 3.4
of arXiv:2109.04389. Moreover, we provide an example (Example A) showing that
the idealiser of a subbrace (as defined in arXiv:2205.01572v2) does not exist
in general.
