In this article, the groups acting on parallelisms in PG(3, q), q = pr, which are generated by collineations of order a p-primitive divisor of q3 − 1 are completely determined. In particular, when the group generated is non-solvable only the groups PSL(2,7) or A7 are possible. If the parallelism is transitive then either it is one of the two regular parallelisms in PG(3,2) or the group is solvable and is contained in гL(1,q3)/Z, where Z denotes the scalar group of order q − 1.
Key words and phrasesParallelism projective space translation plane
2000 Mathematics Subject Classification51E23 20B25
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