Finitely presented algebras defined by permutation relations of dihedral type.

The class of finitely presented algebras over a field with a set of generators and defined by homogeneous relations of the form , where runs through a subset of the symmetric group of degree , is investigated. Groups in which the cyclic group is a normal subgroup of index are considered. Certain representations by permutations of the dihedral and semidihedral groups belong to this class of groups. A normal form for the elements of the underlying monoid with the same presentation as the algebra is obtained. Properties of the algebra are derived, it follows that it is an automaton algebra in the sense of Ufnarovskij. The universal group of is a unique product group, and it is the central localization of a cancellative subsemigroup of . This, together with previously obtained results on such semigroups and algebras, is used to show that the algebra is semiprimitive. [ABSTRACT FROM AUTHOR]