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首页> 外文期刊>Designs, Codes and Crytography >On point-transitive and transitive deficiency one parallelisms of PG(3,4)
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On point-transitive and transitive deficiency one parallelisms of PG(3,4)

机译：关于点-传递和传递不足PG（3,4）的一种并行性

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摘要

A parallelism in PG(n, q)is point-transitive if it has an automorphism group which is transitive on the points. If the automorphism group fixes one spread and is transitive on the remaining spreads, the parallelism corresponds to a transitive deficiency one parallelism. It is known that there are three types of spreads in PG(3,4)-regular, subregular and aregular. A parallelism is regular if all its spreads are regular. In PG(3, 4) no point-transitive parallelisms, no regular ones, and no transitive deficiency one parallelisms have been known. Both point-transitive parallelisms and transitive deficiency one parallelisms must have automorphisms of order 5. We construct all 32,048 nonisomorphic parallelisms with automorphisms of order 5 and classify them by the orders of their automorphism groups and by the types of their spreads. There are 31,832 parallelisms with an automorphism group fixing exactly one spread. Only for four of them the automorphism group is transitive on the remaining spreads. Among the parallelisms we construct there are no regular ones. There are 4,124 parallelisms with automorphisms of order 5 without fixed points, but none of them is point-transitive.
机译：如果PG（n，q）中的并行性具有在点上可传递的自同构组，则它是点可传递的。如果自同构群固定一个扩展并且在其余扩展上具有传递性，则并行性对应于传递性缺陷一个并行性。众所周知，PG（3,4）规则分布，次规则分布和斜面分布有三种类型的扩展。如果所有扩展都是规则的，则并行是规则的。在PG（3，4）中，没有已知的点传递传递性，常规规则和传递性缺陷。点-传递并行性和传递性缺陷1并行性必须具有5级的自同构性。我们构造所有32,048个具有5级自同构性的非同构并行性，并按其同构组的阶次和它们的传播类型对其进行分类。有31,832个并行度，其中一个同构群恰好固定了一个扩展。仅对于其中的四个，同构群在其余点差上具有传递性。在我们构造的并行度中，没有常规的并行度。有4,124个具有5个不等点的自同构性的并行性，但是它们都不是点可传递的。

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