1. 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: 681; Prenosov: 4
 Celotno besedilo (361,54 KB) |
2. Regular maps with primitive automorphism groupsGareth A. Jones, Martin Mačaj, 2025, izvirni znanstveni članek Opis: We classify the regular maps ℳ which have automorphism groups G acting faithfully and primitively on their vertices. As a permutation group G must be of almost simple or affine type, with dihedral point stabilisers. We show that all such almost simple groups, namely all but a few groups PSL2(q), PGL2(q) and Sz(q), arise from regular maps, which are always non-orientable. In the affine case, the maps ℳ occur in orientable and non-orientable Petrie dual pairs. We give the number of maps associated with each group, together with their genus and extended type. Some of this builds on earlier work of the first author on generalised Paley maps, and on recent work of Jajcay, Li, Širáň and Wang on maps with quasiprimitive automorphism groups.
Ključne besede: regular map, automorphism group, primitive, almost simple, affine group
Objavljeno v RUP: 04.11.2025; Ogledov: 815; Prenosov: 4
Celotno besedilo (512,34 KB) |
3. 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: 821; Prenosov: 5
Celotno besedilo (431,19 KB) |
