Residue class-wise affine group
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In mathematics, residue class-wise affine groups are certain permutation groups acting on 
, whose elements are bijective residue class-wise affine mappings.
A mapping 
is called residue class-wise affine if there is a nonzero integer m such that the restrictions of f to the residue classes (mod m) are all affine. This means that for any residue class 
there are coefficients 
such that the restriction of the mapping f to the set 
is given by
.
Residue class-wise affine groups are countable, and they are accessible to computational investigations. 'Many' of them act multiply transitively on or on subsets thereof. Only relatively basic facts about their structure are known so far.
See also the Collatz conjecture, which is an assertion about a surjective, but not injective residue class-wise affine mapping.
[edit] References and external links
- Stefan Kohl. Restklassenweise affine Gruppen. Dissertation, Universität Stuttgart, 2005.
Archivserver Deutsche Bibliothek OPUS-Datenbank (Universität Stuttgart)
