Dear members of GAP Forum,

In connection with my research of lattices of intermediate subroups
I plan to extend GAP by the functions IsPronormal, IsAbnormal etc.
Recall that the subgroup H is said to be pronormal in G iff for any
$x \in G$ the subgroups H and $H^x$ are conjugate already in their join
$\langle H, H^x \rangle $. The case of non-normal subgroup H distinct
from p-subgroup is of prime importance.

Has anybody fulfilled a similar computation? Or maybe somebody else have
such an intention? I would be very grateful for any information related
to this topic.

As for myself, I intend to start from the permutation groups. So it is
interesting to know, in particular, the most efficient way to obtain a
right transversal set for the normalizer of a given permutation group H.

Best wishes,                       Vitaliy Mysovskikh
                                   St. Petersburg