The spectrum for quasigroups with
cyclic automorphisms and additional symmetries
We determine necessary and sufficient conditions for the existence
of a quasigroup of order n having an automorphism consisting of
a single cycle of length m and n-m fixed points, and having
any combination of the additional properties of being idempotent,
unipotent, commutative, semi-symmetric or totally symmetric.
Quasigroups with such additional properties and symmetries are
equivalent to various classes of triple systems.
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