No CrossRef data available.
Article contents
Automorphism groups of covering posets and of dense posets
Published online by Cambridge University Press: 20 January 2009
Extract
Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.
Given a poset (X, ≦), the covering poset (C(X), ≦) consists of the set C(X) of covering pairs, that is, pairs (a, b)∈X2 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 φv = 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
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 35 , Issue 1 , February 1992 , pp. 115 - 120
- Copyright
- Copyright © Edinburgh Mathematical Society 1992
References
REFERENCES
1.Adeleke, S. A., Dummett, M. A. E. and Neumann, Peter M., On a question of Frege's about right-ordered groups, Bull. London Math. Soc. 19 (1987), 513–521.CrossRefGoogle Scholar
2.Babai, László, On the abstract group of automorphisms, in: Combinatorics (Temperley, H. N. V. (ed.), Cambridge Univ. Press, Cambridge, 1981), 1–40.Google Scholar
3.Babai, L. and Duffus, D., Dimension and automorphism groups of lattices, Algebra Universalis 12 (1981), 279–289.CrossRefGoogle Scholar
5.Birkhoff, Garrett, Sobre los grupos de automorfismos, Rev. Un. Mat. Argentina 11 (1946), 155–157.Google Scholar
6.Frucht, R., Lattices with a given abstract group of automorphisms, Canad. J. Math. 2 (1950), 417–419.CrossRefGoogle Scholar
You have
Access