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A construction of cyclic Steiner triple systems of order pn

✍ Scribed by K.T Phelps

Publisher
Elsevier Science
Year
1987
Tongue
English
Weight
230 KB
Volume
67
Category
Article
ISSN
0012-365X

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✦ Synopsis

Phelps

2.1 will produce such a collection for each n -1/> 1. Choose U as in (3.1) above, then B,, =pBn-1 U U is a set of representatives for a CSTS(p"). Since every multiplier m =-1 (modp n'l) is an automorphism of this system f(x)=p"-lx2 +x will be an isomorphism from B,, to another CSTS(p~), B~. Since f(x) fixes the orbits in pBn_~, pB~_t will be a form sub-CSTS(p "-~) in B" and thus any multiplier isomorphism from B~ to B" must first be a multiplier automorphism (modp "-1) of Bn-1. By choice of B,,_~, the multiplier m must be congruent to 1, a m, or tr 4' (modp "-x) but then the multiplier will be a multiplier automorphism for B~.

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