Details

Autor(en) / Beteiligte

• Cao, Yonglin

Titel

Association Schemes and Directed Graphs Determined by Orbitals of General Linear Groups Over Finite Chain Rings

Ist Teil von

• Communications in algebra, 2010-12, Vol.39 (1), p.220-236

Ort / Verlag

Taylor & Francis Group

Erscheinungsjahr

2010

Quelle

Taylor & Francis Journals Auto-Holdings Collection

Beschreibungen/Notizen

• Let R be a finite commutative chain ring, 1 ≤ k ≤ n − 1, the set of right invertible k × n matrices, and GL n (R) the general linear group of degree n over R, respectively. It is clear that Q ↦ QU ( , U ∈ GL n (R)) is a transitive action on and induces the diagonal action of GL n (R) on defined by (Q 1 , Q 2 )U = (Q 1 U, Q 2 U) for and U ∈ GL n (R), which are then subdivided into orbits under the action of GL n (R). First, we investigate the three questions: (i) How should the orbits be described? (ii) How many orbits are there? (iii) What are the lengths of the orbits? Then we compute parameters of the association scheme on and give precisely the structures of directed graphs determined by the orbits of diagonal action of GL n (R) on .