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A parallelism in $$PG(n,q)$$ P G ( n , q ) is transitive if it has an automorphism group which is transitive on the spreads. A parallelism is regular if all its spreads are regular. In $$PG(3,4)$$ P G ( 3 , 4 ) no examples of transitive and no regular parallelisms are known. Transitive parallelisms in $$PG(3,4)$$ P G ( 3 , 4 ) must have automorphisms of(More)