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Groups of automorphisms of linearly ordered sets: Corrigenda

Published online by Cambridge University Press:  17 April 2009

J.L. Hickman
J.L. Hickman
Affiliation:
Department of Mathematics, Institute of Advanced Studies, Australian National University, Canberra, ACT.
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Abstract

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Dr Isidore Fleischer has shown by a very simple counterexample [1] that Theorem 9 (p. 30) of my paper [3] is incorrect. The error occurs in the proof of Theorem 8, and is due to my having interpreted certain group constructions as cartesian products, whereas they are in fact wreath products. The correct version of Theorem 8 is obtained by replacing cartesian products with wreath products in the appropriate places in Definition 5. The result, however, is easier to see than to state.

Type
Corrigenda
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 2 , April 1977 , pp. 317 - 318
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Fleischer, Isidore, “The automorphism group of a scattered set can be non-commutative”, Bull. Austral. Math. Soc. 16 (1977), 306.CrossRefGoogle Scholar
[2]Hausdorff, F., “Grundzüge einer Theorie der geordneten Mengen”, Math. Ann. 65 (1908), 435–505.CrossRefGoogle Scholar
[3]Hickman, J.L., “Groups of automorphisms of linearly ordered sets”, Bull. Austral. Math. Soc. 15 (1976), 13–32.CrossRefGoogle Scholar