Enumerating regular objects with a given automorphism group
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.
scientific article; zbMATH DE number 4109015