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# 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.identifier.uri https://hdl.handle.net/1920/8651 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.language.iso en en_US dc.subject zero sum en_US dc.subject isomorphism en_US dc.subject symmetric group en_US dc.subject group partition en_US dc.subject Davenport Constant en_US dc.title Zero Sum Properties in Groups en_US dc.type Thesis en thesis.degree.name Master of Science in Mathematics en_US thesis.degree.level Master's en thesis.degree.discipline Mathematics en thesis.degree.grantor George Mason University en
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