1. 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: 375; Prenosov: 1
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3. On split liftings with sectional complementsAleksander Malnič, Rok Požar, 2018, izvirni znanstveni članek Ključne besede: algorithm, Cayley voltages, covering projection, graph, group presentation, invariant section, lifting automorphisms, linear systems over the integers, split extension
Objavljeno v RUP: 02.03.2018; Ogledov: 5086; Prenosov: 181
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4. On the split structure of lifted groupsAleksander Malnič, Rok Požar, 2016, izvirni znanstveni članek Opis: Let ▫$\wp \colon \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations ▫$\rm{CT}_\wp$▫ being abelian. Assuming that a group of automorphisms ▫$G \le \rm{Aut} X$▫ lifts along $\wp$ to a group ▫$\tilde{G} \le \rm{Aut} \tilde{X}$▫, the problem whether the corresponding exact sequence ▫$\rm{id} \to \rm{CT}_\wp \to \tilde{G} \to G \to \rm{id}$▫ splits is analyzed in detail in terms of a Cayley voltage assignment that reconstructs the projection up to equivalence. In the above combinatorial setting the extension is given only implicitly: neither ▫$\tilde{G}$▫ nor the action ▫$G\to \rm{Aut} \rm{CT}_\wp$▫ nor a 2-cocycle ▫$G \times G \to \rm{CT}_\wp$▫, are given. Explicitly constructing the cover ▫$\tilde{X}$▫ together with ▫$\rm{CT}_\wp$▫ and ▫$\tilde{G}$▫ as permutation groups on ▫$\tilde{X}$▫ is time and space consuming whenever ▫$\rm{CT}_\wp$▫ is large; thus, using the implemented algorithms (for instance, HasComplement in Magma) is far from optimal. Instead, we show that the minimal required information about the action and the 2-cocycle can be effectively decoded directly from voltages (without explicitly constructing the cover and the lifted group); one could then use the standard method by reducing the problem to solving a linear system of equations over the integers. However, along these lines we here take a slightly different approach which even does not require any knowledge of cohomology. Time and space complexity are formally analyzed whenever ▫$\rm{CT}_\wp$▫ is elementary abelian.
Ključne besede: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product
Objavljeno v RUP: 15.10.2015; Ogledov: 4494; Prenosov: 171
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5. A rhizome as a map of a rupture of the cartesian dualismKatja Cergolj Edwards, 2008, izvirni znanstveni članek Opis: This essay explores the potentiality of organizing the immediate reality of lived experience of modern individual through a construct of Deleuze' and Guattari's rhizome. This practice, claimed in this essay, negates the traditional construction of knowledge, based on Cartesian perspectivalism, and offers nomadic identities of postcolonial world prospective of active, performative construction of personal bricolages
Ključne besede: postcolonialism, dualism, identity, cartesian, rhizome, re-presentation, multiplicity, nomadism, performativity
Objavljeno v RUP: 10.07.2015; Ogledov: 3909; Prenosov: 35
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