In:
Proceedings of the Edinburgh Mathematical Society, Cambridge University Press (CUP), Vol. 35, No. 1 ( 1992-02), p. 115-120
Abstract:
Given a poset ( X , ≦), the covering poset ( C ( X ), ≦) consists of the set C ( X ) of covering pairs, that is, pairs ( a, b )∈ X 2 with a 〈 b such that there is no c ∈ X with a 〈 c 〈 b , partially ordered by ( a, b )≦( a′, b′ ) if and only if ( a, b ) = ( a′, b′ ) or b ≦ a′ . There is a natural homomorphism v from the automorphism group of ( X , ≦) into the automorphism group of ( C ( X ), ≦). It is shown that given groups G, H and a homomorphism α from G into H there exists a poset ( X , ≦) and isomorphisms φψ from G onto Aut( X , ≦), respectively from H onto Aut( C ( X ), ≦) such that φ v = αψ. It is also shown that every group is isomorphic to the automorphism group of a poset all of whose maximal chains are isomorphic to the nationals.
Type of Medium:
Online Resource
ISSN:
0013-0915
,
1464-3839
DOI:
10.1017/S001309150000537X
Language:
English
Publisher:
Cambridge University Press (CUP)
Publication Date:
1992
detail.hit.zdb_id:
1465484-2
SSG:
17,1
