Groups with elements of order 8 do not have the DCI property
| dc.contributor.author | Dobson, Ted | |
| dc.contributor.author | Morris, Joy | |
| dc.contributor.author | Spiga, Pablo | |
| dc.date.accessioned | 2025-12-04T22:24:06Z | |
| dc.date.available | 2025-12-04T22:24:06Z | |
| dc.date.issued | 2025 | |
| dc.description | Open access article. Creative Commons Attribution license (CC BY 4.0) applies | |
| dc.description.abstract | Let k be odd, and n an odd multiple of 3. Although this can also be deduced from known results, we provide a new proof that Ck ⋊ C₈ and (Cn × C₃) ⋊ C₈ do not have the Directed Cayley Isomorphism (DCI) property. When k is prime, Ck ⋊ C₈ had previously been proved to have the Cayley Isomorphism (CI) property. To the best of our knowledge, the groups Cp ⋊ C₈ (where p is an odd prime) are only the second known infinite family of groups that have the CI property but do not have the DCI property. This also provides a new proof of the result (which follows from known results but was not explicitly published) that no group with an element of order 8 has the DCI property. One piece of our proof is a new result that may prove to be of independent interest: we show that if a permutation group has a regular subgroup of index 2 then it must be 2-closed. | |
| dc.description.peer-review | Yes | |
| dc.identifier.citation | Dobson, T., Morris, J., & Spiga, P. (2025). Groups with elements of order 8 do not have the DCI property. The Art of Discrete and Applied Mathematics, 8(2), Article #P2.08. https://doi.org/10.26493/2590-9770.1549.3cb | |
| dc.identifier.uri | https://hdl.handle.net/10133/7236 | |
| dc.language.iso | en | |
| dc.publisher | University of Primorska | |
| dc.publisher.department | Department of Mathematics and Computer Science | |
| dc.publisher.faculty | Arts and Science | |
| dc.publisher.institution | University of Primorska | |
| dc.publisher.institution | University of Lethbridge | |
| dc.publisher.institution | University of Milano-Bicocca | |
| dc.publisher.url | https://doi.org/10.26493/2590-9770.1549.3cb | |
| dc.subject | CI property | |
| dc.subject | DCI property | |
| dc.subject | Cayley graphs | |
| dc.subject | Cayley digraphs | |
| dc.subject | 2-closed groups | |
| dc.title | Groups with elements of order 8 do not have the DCI property | |
| dc.type | Article |