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Dear GAP-Forum,

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.

Many regards,

Peter Mayr

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