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- W2041625336 abstract "Let ε, Λ, Λ*, Λ R stand for the set of non-negative integers, isols, isolic integers and regressive isols respectively, and let P(τ) be the ω-group of Gödel numbers of permutations of the set τ ε ε which move only finitely many elements of τ. The concept of an ω-group was studied by Hassett [5]. He proved in P12 of [5] that for an isolated set τ, the decomposition of P (τ) into conjugacy sets is a gc -decomposition if and only if τ is regressive. For the finite symmetric group on n elements, S n it is known that the order of the conjugacy class is p(n) , where p(n) is the partition function. The author shows in this paper, using a result of Barback [1], that if p Λ( T ) is Nerode's canonical extension of p(n) to Λ and Req (τ) = T , then pΛ( T ) = Req C τ , where C τ is the decomposition of P (τ) into conjugacy sets. The reader is assumed to be familiar with the contents of [2], [4] and [5]." @default.
- W2041625336 created "2016-06-24" @default.
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- W2041625336 date "1973-03-01" @default.
- W2041625336 modified "2023-09-27" @default.
- W2041625336 title "The recursive equivalence type of a decomposition of an ω-group: The RET of a decomposition" @default.
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- W2041625336 doi "https://doi.org/10.1017/s1446788700012921" @default.
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