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A note on “automorphism groups of partial orders”

✍ Scribed by M.G. Stone

Publisher
Elsevier Science
Year
1978
Tongue
English
Weight
235 KB
Volume
22
Category
Article
ISSN
0012-365X

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✦ Synopsis

We refer to articles by Bird [I] and Bird et al. [2] on automorphisms ol' posets. Let P, Q de-ote posets; P x Q is the Cartesian product with the lexicographic order and R&Q that same product with the "reverse" lexicographic order, viz. (p, -1) < (a', 9') iff 4 < q' or q = 4' and p *f p'. r(P) denotes the automorphism group of P, i.e. all order preserving maps of P onto P which have order preserving inverses. The wreath product r(Q) 1 r(P) is the group of permutations cf the csrtesian product of P with Q given by pairs (b, f) with b E T(P) and f~ (I'! uJ>)~ lvhich act on (p, q)~ PX Q by (b, f)(p, 9) = (b(p), f,(s)). The terminology and notatk3rl is essentially that found in [2], where the following rssult is established:

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