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We give a rough sketch of the objects we are concerned with and of their
interdependencies. Planar near-rings have been used to obtain certain
BIB-designs [Fer70].
Finite planar near-rings can be constructed from an
additive group and a group of automorphisms of which act
fixed-point-freely on (see [AC68,Cla92,Pil83]).
This fact links planar near-rings and Frobenius groups. Each Frobenius group
is a semi-direct product of a group , the Frobenius kernel, which is
normal, and a fixed-point-free automorphism group , the Frobenius complement
[Hup67].
Fixed-point-free automorphism groups also occur in the characterization of
finite simple zero-symmetric near-rings with identity. Such a near-ring is
either a ring or isomorphic to a centralizer near-ring,

where is a fixed-point-free automorphism group on the group .
We plan to investigate the connections between near-rings, Frobenius groups
and designs. One goal is to reduce the properties of seemingly distinct
algebraic structures to one underlying concept, namely that of Frobenius
groups/fixed-point-free automorphism groups. This approach is meant to bridge the gaps
between classical topics which were investigated independently in the past.

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** Up:** 2.1 State of the
** Previous:** 2.1 State of the
Peter Mayr
2002-08-12