Enumerating regular objects with a given automorphism group
type: Item
instance of: scholarly article
title: Enumerating regular objects with a given automorphism group
zbMATH Open document ID: 0677.20032
DOI: 10.1016/0012-365X(87)90199-3
author: M. L. N. Downs
author: Gareth Jones
published in: Discrete Mathematics
publication date: 1987-01-01T00:00:00Z
review text: In certain combinatorial categories, e.g. oriented maps on surfaces [the second author and \textit{D. Singerman}, Proc. Lond. Math. Soc., III. Ser. 37, 273-307 (1978; Zbl 0391.05024)], the regular objects, with finite symmetry group G, are in one-to-one correspondence with normal subgroups with quotient G of particular groups \(\Gamma\), frequently free products: In the above example, \(\Gamma ={\mathbb{Z}}_ 2*{\mathbb{Z}}\). For \(G=PSL_ 2(q)\), q prime and certain \(\Gamma\), the enumeration of these subgroups has been carried out by \textit{P. Hall} [Q. J. Math., Oxf. II. Ser. 7, 134-151 (1936; Zbl 0014.10402)]. The authors indicate the extension to the case \(q=2^ e\) for groups \(\Gamma\) arising in categories related to the example given above.
Mathematics Subject Classification ID: 20H15
Mathematics Subject Classification ID: 20E07
Mathematics Subject Classification ID: 20E06
Mathematics Subject Classification ID: 20F29
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 05A15
zbMATH DE Number: 4109015
zbMATH Keywords: combinatorial categories
zbMATH Keywords: regular objects
zbMATH Keywords: symmetry groups
zbMATH Keywords: free products
zbMATH Keywords: subgroups
MaRDI profile type: Publication
cites work: FOUNDATIONS OF THE THEORY OF MAPS ON SURFACES WITH BOUNDARY
cites work: Q4071773
cites work: Q3855356
cites work: Q3251484
cites work: Theory of Maps on Orientable Surfaces
cites work: Operations on maps, and outer automorphisms
description: scientific article; zbMATH DE number 4109015