Geodesic
THE SYMMETRIC GENUS OF 2-GROUPS
Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 9-21

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DOI

Let G be a finite group. The symmetric genus σ(G) is the minimum genus of any Riemann surface on which G acts faithfully. We show that if G is a group of order 2m that has symmetric genus congruent to 3 (mod 4), then either G has exponent 2m−3 and a dihedral subgroup of index 4 or else the exponent of G is 2m−2. We then prove that there are at most 52 isomorphism types of these 2-groups; this bound is independent of the size of the 2-group G. A consequence of this bound is that almost all positive integers that are the symmetric genus of a 2-group are congruent to 1 (mod 4).
DOI : 10.1017/S0017089512000316
Mots-clés : Primary 20F38, Secondary 20D15, 20H10, 30F99, 57M60 
MAY, COY L.; ZIMMERMAN, JAY. THE SYMMETRIC GENUS OF 2-GROUPS. Glasgow mathematical journal, Tome 55 (2013) no. 1, pp. 9-21. doi: 10.1017/S0017089512000316
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