20.500.12556/RUP-21991 Regular and semi-regular representations of groups by posets Regularne in polregularne predstavitve grup z delno urejenimi množicami 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. automorphism group of posets Cayley graph Dehn presentation simple groups random groups grupa avtomorfizmov delno urejene množice Cayleyjev graf Dehnova predstavitev enostavne grupe slučajne grupe true false true Založba Univerze na Primorskem Angleški jezik Slovenski jezik Članek v reviji 2025-10-21 22:11:33 2025-10-21 22:11:33 2025-11-11 03:07:29 0000-00-00 00:00:00 2025 0 0 18 str. no. 2, [article no.] P2.06 Vol. 25 2025 0000-00-00 Zaloznikova Objavljeno NiDoloceno 0000-00-00 0000-00-00 2025-03-13 51 1855-3974 https://doi.org/10.26493/1855-3974.3312.bb7 AMC_Barmak_2025.pdf AMC_Barmak_2025.pdf 1 E6C7CF9AF8576811C4658AB76800E6A0 0e726777d987d43d954ea5b7fbfd95c44ab51efea29019c28b514ba162019f67 10a24b62-aebb-11f0-8f0b-005056ac49c0 https://repozitorij.upr.si/Dokument.php?lang=slv&id=31926 Založba Univerze na Primorskem 0 0 0