[HTML][HTML] The spectrum for quasigroups with cyclic automorphisms and additional symmetries
D Bryant, M Buchanan, IM Wanless - Discrete mathematics, 2009 - Elsevier
D Bryant, M Buchanan, IM Wanless
Discrete mathematics, 2009•ElsevierWe 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.
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.
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.
Elsevier
