Cyclic parallelisms of PG(5, 2)

摘要

.A spread is a set of lines of PG(d, q), which partition the point set. A parallelism of PG(d. q) is a partition of the set of lines by spreads. A parallelism is cyclic if there is an automorphism which permutes its spreads in one cycle. In the present paper a classification by computer search of all cyclic parallelisms of PG(5, 2) is presented. It is established that there are 1090494 nonisomorphic cyclic parallelisms, among which 286 ones with full automorphism group of order 155 (this result coincides with a result of Stinson and Vanstone [15]), and the rest with full automorphism group of order 31.