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The automorphism group of a scattered set can be non-commutative

Published online by Cambridge University Press:  17 April 2009

Isidore Fleischer
Isidore Fleischer
Affiliation:
Centre de recherches mathématiques, Université de Montréal, Montréal, Canada.
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Abstract

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Perhaps the simplest example is the lexicographic sum of copies Zn of the integers indexed by the integers. If one performs the shift in the 0-indexed summand m0 → (m+1)0 while leaving all the other summands fixed, and follows this with the shift Zn → Zn+1 in the index set, then the element 00. will be sent on 11; whereas under these automorphisms performed in the other order, it will be sent on 01. This non-commutativity contradicts Theorem 9 in [1].

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 2 , April 1977 , pp. 306
Copyright
Copyright © Australian Mathematical Society 1977

References

[1]Hickman, J.L., “Groups of automorphisms of linearly ordered sets”, Bull. Austral. Math. Soc. 15 (1976), 13–32.CrossRefGoogle Scholar