Finite generability of some groups of recursive permutations
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S. A. Volkov
Abstract
Let a class 𝑸 of functions of natural argument be closed with respect to a superposition and contain the identity function. The set of permutations ƒ such that ƒ, ƒ–1 ∈ 𝑸 forms a group (with respect to the operation of composition) which we denote by Gr(𝑸). We prove the finite generability of Gr(𝑸) for a large family of classes 𝑸 satisfying some conditions. As an example, we consider the class FP of functions which are computable in polynomial time by a Turing machine. The obtained result is generalised to the classes 
of the Grzegorczyk system, n ≥ 2.
It is proved that for the considered classes 𝑸 the minimum number of permutations generating the group Gr(𝑸) is equal to two. More exactly, there exist two permutations of the given group such that any permutation of this group can be obtained by compositions of these permutations.
© de Gruyter 2008
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- On stability of a vector combinatorial problem with MINMIN criteria
- On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence
- Characteristics of random systems of linear equations over a finite field
- On the realisation of Boolean functions by informational graphs
- Estimates of the number of occurrences of vectors on cycles of linear recurring sequences over a finite field
- Finite generability of some groups of recursive permutations
- Independent systems of generators and the Hopf property for unary algebras
- Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay
- On ranks, Green classes, and the theory of determinants of Boolean matrices
Articles in the same Issue
- On stability of a vector combinatorial problem with MINMIN criteria
- On the asymptotic behaviour of the probability of existence of equivalent tuples with nontrivial structure in a random sequence
- Characteristics of random systems of linear equations over a finite field
- On the realisation of Boolean functions by informational graphs
- Estimates of the number of occurrences of vectors on cycles of linear recurring sequences over a finite field
- Finite generability of some groups of recursive permutations
- Independent systems of generators and the Hopf property for unary algebras
- Estimates of the complexity of approximation of continuous functions in some classes of determinate functions with delay
- On ranks, Green classes, and the theory of determinants of Boolean matrices
