1. Some new compatible groupsZhaochen Ding, Gabriel Verret, 2026, izvirni znanstveni članek Opis: Two finite groups $L_1$ and $L_2$ are compatible if there exists a finite group $G$ with isomorphic normal subgroups $N_1$ and $N_2$ such that $L_1 \cong G/N_1$ and $L_2 \cong G/N_2$. We prove a new sufficient condition for two groups to be compatible. As a corollary, we obtain that nilpotent groups of the same order are compatible, and so are groups of the same square-free order.
Ključne besede: compatibility, finite nilpotent groups, p-groups
Objavljeno v RUP: 20.03.2026; Ogledov: 204; Prenosov: 6
 Celotno besedilo (1,49 MB)
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3. On simple groups that admit a string C-group representationDimitri Leemans, Adrien Vandenschrick, 2026, izvirni znanstveni članek Opis: We prove that a simple group admits at least one string C-group representation if and only if it is not one of PSL(3, q), PSU(3, q),
PSL(4, 2^n), PSU(4, 2^n), PSU(4, 3), PSU(5, 2), A₆, A₇, M₁₁, M₂₂, M₂₃ or McL.
Ključne besede: simple groups, string C-groups
Objavljeno v RUP: 05.01.2026; Ogledov: 467; Prenosov: 0
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4. Groups with elements of order 8 do not have the DCI propertyTed Dobson, Joy Morris, Pablo Spiga, 2025, izvirni znanstveni članek 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: 428; Prenosov: 2
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5. On the wreath product of signed and gain graphs and its spectrumMatteo Cavaleri, Alfredo Donno, Stefano Spessato, 2025, izvirni znanstveni članek Opis: We introduce a notion of wreath product of two gain graphs (Γ_1, ψ_1, G_1) and (Γ_2, ψ_2, G_2), producing a gain graph over the direct product group G_2|V_Γ1| × G_1, whose underlying graph is the classical wreath product of graphs Γ_1≀Γ_2. By composition with a suitable group homomorphism, our construction produces a signed graph when the two factors are signed graphs. We prove that the wreath product is stable under switching isomorphism. By using group representations, we are able to perform spectral computations on the wreath product: in particular, we determine its largest and its smallest eigenvalue, and we give a description of the spectrum when the first factor is a complex unit complete balanced or antibalanced gain graph, and the second factor is circulant. Finally, when G_1 is a group of permutations of the vertex set of the first factor, and the group G_2 is abelian, we give an alternative definition producing a gain graph over the group wreath product G_1≀G_2, which turns out to be stable under switching equivalence of the second factor, when the first factor is balanced.
Ključne besede: gain graph, signed graph, wreath product of graphs, wreath product of groups, circulant gain graph, mixed Kronecker product, π-spectrum
Objavljeno v RUP: 22.10.2025; Ogledov: 681; Prenosov: 6
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7. Regular and semi-regular representations of groups by posetsJonathan A. Barmak, 2025, izvirni znanstveni članek Opis: By a result of Babai, with finitely many exceptions, every group G admits a semi-regular poset representation with three orbits, that is, a poset P with automorphism group Aut(P) ≃ G such that the action of Aut(P) on the underlying set is free and with three orbits. Among finite groups, only the trivial group and ℤ_2 have a regular poset representation (i.e. semi-regular with one orbit), however many infinite groups admit such a representation. In this paper we study non-necessarily finite groups which have a regular representation or a semi-regular representation with two orbits. We prove that if G admits a Cayley graph which is locally the Cayley graph of a free group, then it has a semi-regular representation of height 1 with two orbits. In this case we will see that any extension of the integers by G admits a regular representation. Applications are given to finite simple groups, hyperbolic groups, random groups and indicable groups.
Ključne besede: automorphism group of posets, Cayley graph, Dehn presentation, simple groups, random groups
Objavljeno v RUP: 21.10.2025; Ogledov: 498; Prenosov: 1
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10. Social mechanisms to engage visitors in cultural heritage monuments preservationAna Slavec, Vesna Starman, Nežka Sajinčič, Gertrud Fábián, László Hajdu, Miklós Ferenz Krész, Anna Malgorzata Sandak, Jakub Michal Sandak, Črtomir Tavzes, 2021, objavljeni povzetek znanstvenega prispevka na konferenci Ključne besede: cultural heritage, focus groups, gamification, ICT, tourism
Objavljeno v RUP: 24.06.2021; Ogledov: 2728; Prenosov: 67
Celotno besedilo (1,75 MB)
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