Geodesic
The inverse of differentiable permutations over groups
Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 30-32.

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The concept of a differentiable function over a group with a normal series generalizing the concept of a polynomial function is introduced. In the case of abelian, nilpotent and solvable groups, a recurrent formula for constructing the inverse of differentiable permutation with respect to composition is proved.
Mots-clés : permutation, polynomial over group
Keywords: differentiable function. 
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A. V. Karpov. The inverse of differentiable permutations over groups. Prikladnaya Diskretnaya Matematika. Supplement, no. 8 (2015), pp. 30-32. http://geodesic.mathdoc.fr/item/PDMA_2015_8_a10/

[1] Anashin V. S., “Noncommutative algebraic dynamics: ergodic theory for profinite groups”, Proc. Steklov Institute of Math., 265, 2009, 30–58 | DOI | MR | Zbl

[2] Karpov A. V., “Perestanovochnye mnogochleny nad primarnymi koltsami”, Prikladnaya diskretnaya matematika, 2013, no. 4(22), 16–21