| Title: | Regular maps with primitive automorphism groups |
|---|
| Authors: | ID Jones, Gareth A. (Author)
ID Mačaj, Martin (Author) |
|---|
| Files: |  ADAM_Jones,Macaj_2025.pdf (512,34 KB)
MD5: 4248E5C26178CE57EDFC5547974D294A
|
|---|
| Language: | English |
|---|
| Work type: | Article |
|---|
| Typology: | 1.01 - Original Scientific Article |
|---|
| Organization: | ZUP - University of Primorska Press
|
|---|
| Abstract: | 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. |
|---|
| Keywords: | regular map, automorphism group, primitive, almost simple, affine group |
|---|
| Publication status: | Published |
|---|
| Publication version: | Version of Record |
|---|
| Publication date: | 13.10.2025 |
|---|
| Publisher: | Založba Univerze na Primorskem |
|---|
| Year of publishing: | 2025 |
|---|
| Number of pages: | 22 str. |
|---|
| Numbering: | Vol. 8, no. 3, [article no.] P3.09 |
|---|
| PID: | 20.500.12556/RUP-22083  |
|---|
| UDC: | 51 |
|---|
| eISSN: | 2590-9770 |
|---|
| DOI: | 10.26493/2590-9770.1602.68f |
|---|
| Publication date in RUP: | 04.11.2025 |
|---|
| Views: | 322 |
|---|
| Downloads: | 2 |
|---|
| Metadata: |    |
|---|
|
:
|
Copy citation |
|---|
| | | | Average score: | (0 votes) |
|---|
| Your score: | Voting is allowed only for logged in users. |
|---|
| Share: |  |
|---|
Hover the mouse pointer over a document title to show the abstract or click
on the title to get all document metadata. |
