Correction to ¿Faithful permutation representations of toroidal regular maps¿ (Journal of Algebraic Combinatorics, (2020), 52, 3, (317-337), 10.1007/s10801-019-00904-8)

• Type: Other Publications
• Date: 2020

Authors

Fernandes, ME (Author) Other; Piedade, CA (Author) Other

Other information

Authenticus ID: P-00T-2WA

DOI: 10.1007/s10801-020-00985-w

Abstract (EN): In [1], we claim that we give a complete list of the possible degrees of a faithful transitive permutation representation of the groups of the toroidal regular maps. Indeed, the list given for type {4, 4} is complete; however, recently we were surprised with the existence of exceptional degrees for the map {3, 6}. After, we struggled to find the reason why there were some degrees missing in our classification. The fact is that there is a gap in one proof, having consequences in two of our main theorems. Our goal is to fill in that gap. In what follows, let G be the group of symmetries of a toroidal regular map of type {4, 4} or {3, 6}, and suppose G is represented as a faithful transitive permutation representation group of degree n. Let T be the translation group generated by unitary independent translations of order s defining the groups of {4, 4}s or {3, 6}s for s ¿ {(s, 0), (s, s)} (see [1]). We recall the following results. Acknowledgements This work is supported by The Center for Research and Development in Mathematics and Applications (CIDMA) through the Portuguese Foundation for Science and Technology (FCT - Fundação para a Ciência e a Tecnologia), references UIDB/04106/2020 and UIDP/04106/2020. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.

Language: English

Type (Professor's evaluation): Scientific