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Associative Binary Operations on a Set with Five Elements

by Amit Sehgal, Ravinder Kumar, Ombir Dahiya
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 76 - Number 6
Year of Publication: 2013
Authors: Amit Sehgal, Ravinder Kumar, Ombir Dahiya
10.5120/13252-0725

Amit Sehgal, Ravinder Kumar, Ombir Dahiya . Associative Binary Operations on a Set with Five Elements. International Journal of Computer Applications. 76, 6 ( August 2013), 27-33. DOI=10.5120/13252-0725

@article{ 10.5120/13252-0725,
author = { Amit Sehgal, Ravinder Kumar, Ombir Dahiya },
title = { Associative Binary Operations on a Set with Five Elements },
journal = { International Journal of Computer Applications },
issue_date = { August 2013 },
volume = { 76 },
number = { 6 },
month = { August },
year = { 2013 },
issn = { 0975-8887 },
pages = { 27-33 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume76/number6/13252-0725/ },
doi = { 10.5120/13252-0725 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:45:12.592191+05:30
%A Amit Sehgal
%A Ravinder Kumar
%A Ombir Dahiya
%T Associative Binary Operations on a Set with Five Elements
%J International Journal of Computer Applications
%@ 0975-8887
%V 76
%N 6
%P 27-33
%D 2013
%I Foundation of Computer Science (FCS), NY, USA
Abstract

Associativity of a binary operation is one of most fundamental property in algebra. The number of binary operation on a set of only five elements is as large as 298,023,223,876,953,125. In this paper, the authors give the answer of the question "How many binary operations on a five elements are associative?" The main goal of this paper is to extend [3] and [5] for five element set.

References
  1. Man-Keung Siu, Which Latin Squares are Cayley Tables?, AMS Monthly , 98 (1991) 625-627
  2. Fri?rik Diego and Krist?n Halla J?nsd?tti? , Associative Operations on a Three-Element Set, TMME, vol 5, nos2 &3 , pp 257-268, 2008
  3. Amit Sehgal and ManMohan , Associative Binary operation on a set with Three elements, International Journal of Essential Sciences, Vol 5, No. 1, pp1-8,2011 (ISSN:0973-8436)
  4. Sarita and Amit Sehgal, Using Partition Calculation for number of associative operation is reduced. Proceeding of International Conference on Mathematics and Soft Computing (Application in Engineering) pp437-446 Dec 4-5,2010
  5. Amit Sehgal, Sarita and Sunil Dua, Associative Binary operation on a set with Four elements, International Journal of Computer Science and Communication Engineering Volume 1 Issue 2 paper id IJCSCE 121204, 2013 (ISSN:2319-7080)
  6. George E. Forsythe, Swac Computers 126 distinct semi groups of order 4 Proc. Amer. Math. Soc. 6 (1955), 443-447.
  7. Lyle Ramshaw, The On-Line Encyclopedia of Integer Sequences -A023814 (Number of associative binary operations on an n-set
  8. A. Distler and T. Kelsey, The semigroups of order 9 and their automorphism groups, arXiv preprint arXiv: 1301. 6023, 2013.
Index Terms

Computer Science
Information Sciences

Keywords

binary operations associativity isomorphism order Partition

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