This paper is a contribution to the classification of parallelisms in three-dimensional projective spaces over small finite fields of order q by computer. The smallest space in which parallelisms have not yet been classified is for \(q=4.\) Partial results are available. The parallelisms admitting a nontrivial automorphism of odd prime order are known. Moreover, much is known about the case of parallelisms of \({{\mathrm{PG}}}(3,4)\) whose automorphism group is a two group. Namely, everything is known for two of the three possible groups of order two, as well as for cyclic groups of order 4. The present paper will settle the case of parallelisms whose automorphism group is elementary abelian of order 4. This leaves open the cases of parallelisms whose full automorphism groups are either trivial or a specific group of order two.

本文对计算机在q阶小有限域上的三维投影空间中的并行性分类做出了贡献。尚未对并行度进行分类的最小空间是对于\(q=4.\)的部分结果可用。承认奇素数阶非平凡自同构的并行性是已知的。此外，我们对\({{\mathrm{PG}}}(3,4)\)的并行性情况了解很多。其自同构群是二群。也就是说，对于三个可能的二阶群中的两个以及四阶循环群，一切都是已知的。本文将解决自同构群是四阶初等阿贝尔的并行性的情况。并行性的完全自同构群要么是平凡的要么是特定的二阶群。