Document Type
Article
Publication Title
Acta Mathematica Hungarica
Publication Date
2026
Keywords
Herzog–Schönheim conjecture, Steiner coset partition, Transversal coset parallelism, (affine) vector space partition
Abstract
A Steiner coset partition of a group G with respect to pairwise distinct subgroups H1 , …, Hr is a collection of pairwise disjoint cosets g1 H1 , …, gr Hr whose union is G. Motivated by the Herzog–Schönheim Conjecture, we have recently started exploring the groups that admit Steiner coset partitions. In previous work, we completely classified such groups for up to r = 4 mutually commuting subgroups. In this paper, we extend the classification to r = 5 mutually commuting subgroups.
Funding Source
This article was published open access thanks to a transformative agreement between Milner Library and Springer Nature.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
DOI
10.1007/s10474-026-01635-
Recommended Citation
Akman, F., & Sissokho, P. (2026). Steiner coset partitions for five mutually commuting subgroups. Acta Mathematica Hungarica. https://doi.org/10.1007/s10474-026-01635-6
Comments
First published in Acta Mathematica Hungarica (2026): https://doi.org/10.1007/s10474-026-01635-6