20.500.12556/RUP-22071 Groups with elements of order 8 do not have the DCI property Grupe z elementi reda 8 nimajo lastnosti DCI 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. CI property DCI property Cayley graphs Cayley digraphs 2-closed groups 2-closure lastnost CI lastnost DCI Cayleyjevi grafi Cayleyjevi digrafi 2-zaprte grupe 2-zaprtje true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-11-03 11:57:40 2025-11-03 11:57:40 2025-11-18 03:05:00 0000-00-00 00:00:00 2025 0 0 5 str. no. 2, [article no.] P2.08 Vol. 8 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-03-25 51 2590-9770 10.26493/2590-9770.1549.3cb ADAM_Dobson,Morris,Spiga_2025.pdf ADAM_Dobson,Morris,Spiga_2025.pdf 1 1C46AD5A0034E1646033C0EC6A41A2C9 aa99164c09bd1ea9b28164e8e5a10c1e36be43045528a17f55666b121151f613 7b26201d-b8a4-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=32016 Založba Univerze na Primorskem 0 0 0