Iskanje po repozitoriju

Opis: 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.
Ključne besede: CI property, DCI property, Cayley graphs, Cayley digraphs, 2-closed groups, 2-closure
Objavljeno v RUP: 03.11.2025; Ogledov: 457; Prenosov: 2
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Ključne besede: isomorphism, DCI-groups, Schur rings
Objavljeno v RUP: 24.11.2021; Ogledov: 2899; Prenosov: 28
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