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The symmetric crosscap number of the groups Cm × Dn

Etayo Gordejuela, J. Javier and Martínez García, Ernesto (2008) The symmetric crosscap number of the groups Cm × Dn. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, 138 (6). pp. 1197-1213. ISSN 0308-2105

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Abstract

Every finite group G acts as an automorphism group of some non-orientable Klein surfaces without boundary. The minimal genus of these surfaces is called the symmetric cross-cap number and denoted by ˜σ(G). This number is related to other parameters defined on surfaces as the symmetric genus and the strong symmetric genus. The systematic study of the symmetric cross-cap number was begun by C. L. May, who also calculated it for certain finite groups. Here we obtain the symmetric cross-cap number for the groups Cm ×Dn. As an application of this result, we obtain arithmetic sequences of integers which are the symmetric cross-cap number of some group. Finally, we recall the several different genera of the groups Cm × Dn.


Item Type:Article
Uncontrolled Keywords:Automorphism groups; Klein surfaces; cross-cap numbers
Subjects:Sciences > Mathematics > Group Theory
ID Code:15812
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Last Modified:06 Feb 2014 10:32

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