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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Varieties of automorphism groups of orders


Author: W. Charles Holland
Journal: Trans. Amer. Math. Soc. 288 (1985), 755-763
MSC: Primary 06F15; Secondary 08B20, 20B27, 20E10, 20F16
MathSciNet review: 776402
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Abstract: The group $ A(\Omega )$ of automorphisms of a totally ordered set $ \Omega $ must generate either the variety of all groups or the solvable variety of class $ n$. In the former case, $ A(\Omega )$ contains a free group of rank $ {2^{{\aleph _0}}}$; in the latter case, $ A(\Omega )$ contains a free solvable group of class $ n - 1$ and rank $ {2^{{\aleph _0}}}$.


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DOI: https://doi.org/10.1090/S0002-9947-1985-0776402-7
Article copyright: © Copyright 1985 American Mathematical Society