I am interested in computing regular automorphism groups on
a given group G, i.e. groups of automorphisms where all mappings
except the identity mapping operate on G without a fixpoint
except the group identity. Does GAP provide any means to find
all these regular automorphism groups for arbitrary, reasonably
small groups G efficiently ( e.g. for the elementary abelian
group of order 25 )?
I want to avoid the straight forward approach of computing
the whole automorphism group of G and testing the representatives
of the conjugacy classes of its subgroups for regularity,
because this is not feasible for a large automorphism group.
Nevertheless I would like to find all regular automorphism
groups up to conjugacy.
I am well aware that this question might be too general for
specific groups G, while it is easy to answer for others.
However it is a crucial problem in the theory of planar nearrings
and I want a solution that is as general as possible.
Are there any GAP-functions or packages for this task already
and if there are none, how can I use existing functions when
writing my own programs.