On maximal subgroups of the group of recursive permutations. (English. Russian original) Zbl 1358.20022
Mosc. Univ. Comput. Math. Cybern. 40, No. 3, 128-132 (2016); translation from Vestn. Mosk. Univ., Ser. XV 2016, No. 3, 32-35 (2016).
Summary: The group \(G_R\) of all permutations belonging to \(R\) is considered for any partially recursively closed class of functions \(R\). It is proved that the group \(G_R\) has a continuum number of maximal subgroups. Examples of constructive maximal subgroups of \(G_R\) are given.
MSC:
| 20E28 | Maximal subgroups |
| 20B35 | Subgroups of symmetric groups |
| 03D20 | Recursive functions and relations, subrecursive hierarchies |
References:
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