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Maxmal Order of NG-Transformation
Version 1
: Received: 3 October 2020 / Approved: 5 October 2020 / Online: 5 October 2020 (10:58:12 CEST)
Version 2 : Received: 19 October 2020 / Approved: 20 October 2020 / Online: 20 October 2020 (11:36:51 CEST)
Version 2 : Received: 19 October 2020 / Approved: 20 October 2020 / Online: 20 October 2020 (11:36:51 CEST)
How to cite: Abdunabi, F. Maxmal Order of NG-Transformation. Preprints 2020, 2020100068. https://doi.org/10.20944/preprints202010.0068.v1 Abdunabi, F. Maxmal Order of NG-Transformation. Preprints 2020, 2020100068. https://doi.org/10.20944/preprints202010.0068.v1
Abstract
In this paper, we consider the problem that the maximal order consider the groups that consisting of transformations we called NG-Transformation on a nonempty set A has no bijection as its element. We find the order of these groups not greater that (n-1)!. In addition, we will prove our result by showing that any kind of NG-group in the theorem be isomorphic to a permutation group on a quotient set of A with respect to an equivalence relation on A.
Keywords
Ng group; permutation group
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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