Steiner Coset Partitions of Groups – ERRATUM

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Fusun Akman and Papa Sissokho, "Steiner Coset Partitions of Groups – ERRATUM," Canadian Mathematical Bulletin, 69(2), 702-702, 2026. https://doi.org/10.4153/s0008439525101392

Local source. The copy read for this card is the held PDF, the one-page erratum (printed p. 702) as downloaded from Cambridge Core; a Markdown reading copy sits beside it. The file prints "© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society. This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited." on its first page, the Creative Commons Attribution 4.0 license.

Corrected article. Akman and Sissokho (2025), Steiner Coset Partitions of Groups.

Correction and scope

The erratum replaces one sentence in the 2025 article's abstract. As the erratum quotes it, the original sentence credited the authors' earlier paper, Transversal coset partitions of groups (Beitr. Algebra Geom. 66 (2025), reference [1] of the article), with ruling out Steiner coset partitions for every number $r\geq 2$ of mutually commuting subgroups $H_i$; the corrected sentence limits this to $r\in\{2,3\}$. The held PDF of the 2025 article, also a Cambridge Core download of 18 September 2026, prints that sentence with $2\leq r\leq 7$ (p. 1359), matching neither version the erratum quotes; for use in this corpus, the erratum's corrected range $r\in\{2,3\}$ controls.

The second correction is typographical. On page 12 of the article (printed p. 1370), the malformed definition of $a_J$ is replaced by

$$a_J\overset{\mathrm{def}}{=}a_1^{j_1}\cdots a_n^{j_n}\in G.$$

The product defining $a_J$ is unchanged, and the held PDF of the article already prints the corrected form.

Consequences for the 2025 paper

The abstract cannot be used as an unconditional nonexistence result for $r\geq 4$ mutually commuting subgroups. In particular, it supplies no such claim for $4\leq r\leq 7$. Uses of the 2025 paper must instead cite its actual result of the required scope: Proposition 2.2 for two distinct proper subgroups, Proposition 2.3 for three distinct proper mutually commuting subgroups, its hypothesis-dependent nonexistence results for larger $r$, or Theorem 2 for the classified $r=4$ case.

The erratum does not alter those numbered results, their proofs, or the paper's constructions. In particular, Theorem 2 still says that four distinct, proper, mutually commuting subgroups admit no Steiner partition unless $G$ is an extension of $C_2\times C_2\times C_2$, and that every such extension does admit one. The conditional results for larger $r$ and the elementary-abelian constructions also remain unaffected; the erratum leaves in place the printed choice of $t$ in Proposition 4.12, whose sign slip the card for the 2025 article records.

Read status. Claims checked against the held PDF. The one-page erratum supplies corrections, not proofs.

Bears on

• Problem 274. The correction narrows a special-case obstruction involving mutually commuting subgroups; it neither resolves the unrestricted exact-covering question nor changes its open status.