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Characterization of finite amenable transformation semigroups: corrigendum
Published online by Cambridge University Press: 09 April 2009
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Theorem 6 of Wilde (1971) is in error. Følner's condition is necessary, but not sufficient, for amenability of a τ-semigroup. For clearly sufficiency would imply that every finite τ-semigroup is amenable, and the simple example on p. 503 of Wilde (1971) shows that this is not so. We refer the reader to Namioka (1964) for a lucid explanation of the fundamental ideas involved.
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- Corrigendum
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- Copyright © Australian Mathematical Society 1975
References
Namioka, I. (1964), ‘Føners's condition for amenable semigroups’, Math. Scand. 15, 18–28.CrossRefGoogle Scholar
Wilde, C. (1973), ‘Characterization of finite amenabled transformation semigroups’, J. Ausral Math. Soc. 15, 86–93.CrossRefGoogle Scholar
Wilde, C., Jayachandran, T. (1971), ‘Amenable transformation semigroups’, J. Austral. Math. Soc. 12, 502–510.CrossRefGoogle Scholar
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