TY - JOUR
T1 - Concerning multiplier automorphisms of cyclic Steiner triple systems
AU - Colbourn, Charles J.
AU - Mendelsohn, Eric
AU - Praeger, Cheryl E.
AU - Tonchev, Vladimir D.
PY - 1992/9
Y1 - 1992/9
N2 - A cyclic Steiner triple system, presented additively over Zv as a set B of starter blocks, has a non-trivial multiplier automorphism λ ≠ 1 when λB is a set of starter blocks for the same Steiner triple system. When does a cyclic Steiner triple system of order v having a nontrivial multiplier automorphism exist? Constructions are developed for such systems; of most interest, a novel extension of Netto's classical construction for prime orders congruent to 1 (mod 6) to prime powers is proved. Nonexistence results are then established, particularly in the cases when v = (2β + 1)α, when v = 9 p with p ≡ 5 (mod 6), and in certain cases when all prime divisors are congruent to 5 (mod 6). Finally, a complete solution is given for all v < 1000, in which the remaining cases are produced by simple computations.
AB - A cyclic Steiner triple system, presented additively over Zv as a set B of starter blocks, has a non-trivial multiplier automorphism λ ≠ 1 when λB is a set of starter blocks for the same Steiner triple system. When does a cyclic Steiner triple system of order v having a nontrivial multiplier automorphism exist? Constructions are developed for such systems; of most interest, a novel extension of Netto's classical construction for prime orders congruent to 1 (mod 6) to prime powers is proved. Nonexistence results are then established, particularly in the cases when v = (2β + 1)α, when v = 9 p with p ≡ 5 (mod 6), and in certain cases when all prime divisors are congruent to 5 (mod 6). Finally, a complete solution is given for all v < 1000, in which the remaining cases are produced by simple computations.
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U2 - 10.1007/BF00141968
DO - 10.1007/BF00141968
M3 - Article
AN - SCOPUS:34249843617
SN - 0925-1022
VL - 2
SP - 237
EP - 251
JO - Designs, Codes and Cryptography
JF - Designs, Codes and Cryptography
IS - 3
ER -