A Steiner Triple System of order v (briefly STS(v)) is 1-rotational under G if it admits G as an automorphism group acting sharply transitively on all but one point.The spectrum of values of v for which there exists a1-rotational STS(v) under a cyclic, an abelian, or a generalized quaternion group, has beenestablished in 1981 (phelps and Rosa), in 2001 (Buratti) and in 2008 (Mishima), respectively.Nevertheless, the spectrum of values of v for which there exists a1-rotational STS(v) under an arbitrary group has not been completely determined yet.This paper is a considerable step forward to the solution of this problem.In fact, we leave as uncertain cases only those for which we have v = (p^3-p)n + 1 = 1 (mod 96)with p a prime, n =1,2,3 mod 4, and the odd part of (p^3-p)n that is square-free and without prime factors congruent to 1 mod 6.

Some progress on the existence of 1-rotational Steiner Triple Systems / Bonvicini, Simona; M., Buratti; Rinaldi, Gloria; T., Traetta. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - STAMPA. - 62:(2012), pp. 63-78. [10.1007/s10623-011-9491-3]

Some progress on the existence of 1-rotational Steiner Triple Systems

BONVICINI, Simona;RINALDI, Gloria;
2012-01-01

Abstract

A Steiner Triple System of order v (briefly STS(v)) is 1-rotational under G if it admits G as an automorphism group acting sharply transitively on all but one point.The spectrum of values of v for which there exists a1-rotational STS(v) under a cyclic, an abelian, or a generalized quaternion group, has beenestablished in 1981 (phelps and Rosa), in 2001 (Buratti) and in 2008 (Mishima), respectively.Nevertheless, the spectrum of values of v for which there exists a1-rotational STS(v) under an arbitrary group has not been completely determined yet.This paper is a considerable step forward to the solution of this problem.In fact, we leave as uncertain cases only those for which we have v = (p^3-p)n + 1 = 1 (mod 96)with p a prime, n =1,2,3 mod 4, and the odd part of (p^3-p)n that is square-free and without prime factors congruent to 1 mod 6.
2012
62
63
78
Some progress on the existence of 1-rotational Steiner Triple Systems / Bonvicini, Simona; M., Buratti; Rinaldi, Gloria; T., Traetta. - In: DESIGNS, CODES AND CRYPTOGRAPHY. - ISSN 0925-1022. - STAMPA. - 62:(2012), pp. 63-78. [10.1007/s10623-011-9491-3]
Bonvicini, Simona; M., Buratti; Rinaldi, Gloria; T., Traetta
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/695468
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