Factoring Elementary p-Groups for p ≤ 7

Sándor Szabó

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DOI: 10.4236/ojdm.2011.11001                

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.

Keywords

Factorization of Finite Abelian Groups, Full-Rank Subset, Full-Rank Factorization, Periodic Subset, Periodic Factorization, Rédei’s Conjecture, Corrádi’s Conjecture

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	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
[2]	K. Corrádi, S. Szabó and P. Hermann, “A character free proof for Rédei's theorem,” Mathematica Pannonica 20 (2009), 3-15.
[3]	P. R. J. ?sterg? rd, “A fast algorithm for the maximum clique problem,” Discrete Applied Mathematics 120 (2002), 195-205.
[4]	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.)
[5]	A. D. Sands, “On the factorisation of finite abelian groups,” Acta Math. Acad. Sci. Hung. 8 (1957), 65-86. doi:10.1007/BF02025232
[6]	S. Szabó and A. D. Sands, “Factoring Groups into Subsets,” CRC Press, Taylor and Francis Group, Boca Raton, 2009.
[7]	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