Work

Deficiency One Parallelisms of PG(5, 2)

Year: 2026

Type: article

Abstract: A spread in PG(n, q) is a set of lines such that each point is in exactly one line. A parallelism is a partition of the set of lines of PG(n, q) to spreads. A deficiency one parallelism is a parallelism with exactly one missing spread. Most of the results on parallelisms are for PG(3, q). PG(5, 2) is the smallest projective space of a dimension greater than 3. All point-transitive and all cyclic parallelisms of PG(5, 2) are known. Parallelisms with some definite automorphism groups have been constructed too. No transitive deficiency one parallelisms are known. The present work concerns deficiency one parallelisms of PG(5, 2). We present all parallelisms of PG(5, 2) which are invariant under a group of order 30 and show that the full automorphism group of a possible transitive deficiency one parallelism of PG(5, 2) cannot have a normal subgroup of order 15.

Source: Mathematics

DOI: 10.3390/math14040687

Authors: Svetlana Topalova, Stela Zhelezova

Institutions: Bulgarian Academy of Sciences, Institute of Mathematics and Informatics

Language: English

Topic: Finite Group Theory Research

Subfield: Discrete Mathematics and Combinatorics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $3,137

Funders: European Commission, Bulgarian National Science Fund