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Symmetries in hexagonal quasigroups

Vladimír Volenec, Mea Bombardelli (2007)

Archivum Mathematicum

Hexagonal quasigroup is idempotent, medial and semisymmetric quasigroup. In this article we define and study symmetries about a point, segment and ordered triple of points in hexagonal quasigroups. The main results are the theorems on composition of two and three symmetries.

Symmetry classes of tensors associated with the semi-dihedral groups S D 8 n

Mahdi Hormozi, Kijti Rodtes (2013)

Colloquium Mathematicae

We discuss the existence of an orthogonal basis consisting of decomposable vectors for all symmetry classes of tensors associated with semi-dihedral groups S D 8 n . In particular, a necessary and sufficient condition for the existence of such a basis associated with S D 8 n and degree two characters is given.

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