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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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$\omega !$ can be a nontrivial automorphism group
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by Judith Roitman PDF
Proc. Amer. Math. Soc. 112 (1991), 623-628 Request permission


Under the axiom "there are ${\omega _1}$ cofinal Cohen reals," the symmetric group on $\omega$ is the nontrivial automorphism group of a thin-tall superatomic Boolean algebra. Certain product groups are also, under the same axiom, nontrivial automorphism groups of thin-tall superatomic Boolean algebras.
  • Alan Dow and Peter Simon, Thin-tall Boolean algebras and their automorphism groups, Algebra Universalis 29 (1992), no. 2, 211–226. MR 1157434, DOI 10.1007/BF01190607
  • Judy Roitman, Superatomic Boolean algebras, Handbook of Boolean algebras, Vol. 3, North-Holland, Amsterdam, 1989, pp. 719–740. MR 991608
  • —, Uncountable autohomeomorphism groups of thin-tall locally compact scattered spaces, preprint.
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Additional Information
  • © Copyright 1991 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 112 (1991), 623-628
  • MSC: Primary 03E35; Secondary 03E05, 06E05, 20B27
  • DOI:
  • MathSciNet review: 1059636