Zero Sum Properties in Groups
| dc.contributor.advisor | Agnarsson, Geir | |
| dc.contributor.author | Wu, Angelina A. | |
| dc.creator | Wu, Angelina A. | |
| dc.date | 2013-12-02 | |
| dc.date.accessioned | 2014-03-09T14:15:41Z | |
| dc.date.available | 2014-03-09T14:15:41Z | |
| dc.date.issued | 2014-03-09 | |
| dc.description.abstract | A conjecture by Erdős and Lemke in elementary number theory goes as follows: If d is a divisor of n and we have d divisors of n, say a1,...,ad, not necessarily distinct, can we always find a subsequence among them such that their sum is (i) divisible by d, and (ii) at most n? -This was proved by Lemke and Kleitman to be indeed the case. They also noted that an equivalent version of their theorem, stated in terms of the additive cyclic group G = Zn is as follows: Every sequence of n elements of G, not necessarily distinct, contains a subsequence g1,...,gk such that g1+...+gk = 0 and Σki=1/|gi|<=1. This has been shown to be correct for every nite abelian group G. Hence a natural question is therefore if this holds true for any finite group G. By the aid of a computer this has been verified for all solvable groups of order 21 or less, but it is still not known whether it holds for all finite groups. - This paper proves that some well-known non-abelian groups have this property, for example the alternating groups An and symmetric groups Sn for n = 3,4,5,6, the dihedral group Dn for every n and the dicyclic group of every order. Some speculations on possible plan of attack for Sn for larger n are finally discussed. | |
| dc.identifier.uri | https://hdl.handle.net/1920/8651 | |
| dc.language.iso | en | |
| dc.subject | Zero sum | |
| dc.subject | Isomorphism | |
| dc.subject | Symmetric group | |
| dc.subject | Group partition | |
| dc.subject | Davenport Constant | |
| dc.title | Zero Sum Properties in Groups | |
| dc.type | Thesis | |
| thesis.degree.discipline | Mathematics | |
| thesis.degree.grantor | George Mason University | |
| thesis.degree.level | Master's | |
| thesis.degree.name | Master of Science in Mathematics |