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Zero Sum Properties in Groups

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dc.contributor.advisor Agnarsson, Geir Wu, Angelina A.
dc.creator Wu, Angelina A. 2013-12-02 2014-03-09T14:15:41Z 2014-03-09T14:15:41Z 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.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 Master of Science in Mathematics en_US Master's en Mathematics en George Mason University en

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