Automorphisms of lexicographic products

✍ Scribed by Elliot Bird; Curtis Greene; Daniel J. Kleitman

• Publisher: Elsevier Science
• Year: 1975
• Tongue: English
• Weight: 908 KB
• Volume: 11
• Category: Article
• ISSN: 0012-365X
• DOI: 10.1016/0012-365x(75)90036-9

✦ Synopsis

The automorphism group i'(P) of a partially ordered set P con Gists of all permutations on P that preserve order (and have order preserving inverses). 111 this paper we raise, amd partially answer, the question: How is the automorphism group of the lexicographic product (Px Qy of two orders (P and Q) related to the automorphism groups of the factors, P and Q?

We show that the wreath product r(Q) wr p(P) is always contained in I'YP X Ql. We find necessary and sufficient conditions for r(P x &) to equal I'((?'I wr r(P ), and when ,Pand Q are finite, q#e find a complete characterization of r(PX Q) in terms of r'(P). I'@) and properties of P and Q.