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 OJDM  Vol.7 No.2 , April 2017
Non-Full Rank Factorization of Finite Abelian Groups
Khalid Amin
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Abstract: Tilings of p-groups are closely associated with error-correcting codes. In [1], M. Dinitz, attempting to generalize full-rank tilings of  Zn2  to arbitrary finite abelian groups, was able to show that if p ≥5, then Znp  admits full-rank tiling and left the case p=3, as an open question. The result proved in this paper the settles of the question for the case p=3.
Keywords: Factorization of Abelian Groups, Error-Correcting Codes
Cite this paper: Amin, K. (2017) Non-Full Rank Factorization of Finite Abelian Groups. Open Journal of Discrete Mathematics, 7, 51-53. doi: 10.4236/ojdm.2017.72005.
References

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https://doi.org/10.1137/S0895480104445794

[2]   Fraser, O. and Gordon, B. (1977) Solution to a Problem by A.D. Sands. Glasgow Mathematical Journal, 20, 115-117.

[3]   Hajós, G. (1949) Sur la factorisation des groupe abeliens, Casopis Pest. Ma. Fys., 74, 157-162.

[4]   Rédei, L. (1965) Die neue Theorie der endlihen abelschen und verallgemeinerung des hauptsatze von Hajos. Acta Mathematica Hungarica, 16, 329-373.
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[5]   Sands, A.D. and Szabo, S. (1991) Factorization of Periodic Subset. Acta Mathematica Hungarica, 57, 159-1167.
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[6]   Szabo, S. (2004) Topics in Factorization of Abelian Groups, Birkhauser, Beijing.

 
 
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