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Moscow Mathematical Journal

Volume 17, Issue 3, July–September 2017  pp. 357–369.

Filling Gaps of the Symmetric Crosscap Spectrum

Authors:  A. Bacelo (1), J. J. Etayo (1), and E. Martínez (2)
Author institution:(1) Departamento de Álgebra, Facultad de Matemáticas, Universidad Complutense. 28040-Madrid, SPAIN
(2) Departamento de Matemáticas Fundamentales. UNED. Paseo Senda del Rey 9. 28040-Madrid, SPAIN


Every finite group G acts faithfully on some non-orientable unbordered surfaces. The minimal topological genus of those surfaces is called the symmetric crosscap number of G. It is known that 3 is not the symmetric crosscap number of any group but it remains unknown whether there are other such values, called gaps.

In this paper we obtain necessary conditions for n to be a gap. According to them, the smallest value of n which could be a gap is in this moment n = 699, and there remain eight possible candidates for n < 2000.

2010 Math. Subj. Class. Primary: 57M60; Secondary: 20F05, 20H10, 30F50.

Keywords: Klein surfaces, automorphism groups, symmetric crosscap number.

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