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Factoring Elementary p-Groups for p ≤ 7
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Open Journal of Discrete Mathematics·Volume 01 (2011)·Pages 1–5·Published 8 April 2011·DOI10.4236/ojdm.2011.11001
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Abstract
It is an open problem if an elementary p-group of rank k ≥ 3 does admit full-rank normalized factorization into two of its subsets such that one of the factors has p elements. The paper provides an answer in the p ≤ 7 special case.
KeywordsFactorization of Finite Abelian GroupsFull-Rank SubsetFull-Rank FactorizationPeriodic SubsetPeriodic FactorizationRédei’s ConjectureCorrádi’s Conjecture
- R. Carraghan and P. M. Pardalos, “An exact algorithm for the maximum clique problem,” Operation Research Letters 9 (1990), 375-382. doi:10.1016/0167-6377(90)90057-C
- K. Corrádi, S. Szabó and P. Hermann, “A character free proof for Rédei's theorem,” Mathematica Pannonica 20 (2009), 3-15.
- P. R. J. ?sterg? rd, “A fast algorithm for the maximum clique problem,” Discrete Applied Mathematics 120 (2002), 195-205.
- L. Rédei, Lückenhafte Polynome über endlichen K?rpern, Birkh?user Verlag, Basel 1970, (English translation: Lacunary Polynomi-als over Finite Fields, North-Holland, Amsterdam, 1973.)
- A. D. Sands, “On the factorisation of finite abelian groups,” Acta Math. Acad. Sci. Hung. 8 (1957), 65-86. doi:10.1007/BF02025232
- S. Szabó and A. D. Sands, “Factoring Groups into Subsets,” CRC Press, Taylor and Francis Group, Boca Raton, 2009.
- S. Szabó and C. Ward, “Factoring elementary groups of prime cube order into subsets,” Mathematics of Computation 67 (1998), 1199-1206. doi:10.1090/S0025-5718-98-00929-6