The symmetric crosscap number of a group
Glasgow mathematical journal, Tome 43 (2001) no. 3, pp. 399-410
Voir la notice de l'article provenant de la source Cambridge University Press
Let G be a finite group. The symmetric crosscap number \tilde \sigma (G) is the minimum topological genus of any compact non-orientable surface (with empty boundary) on which G acts effectively. We first survey some of the basic facts about the symmetric crosscap number; this includes relationships between this parameter and others. We obtain formulas for the symmetric crosscap number for three families of groups, the dicyclic groups, the abelian groups with most factors in the canonical form isomorphic to Z_(2), and the hamiltonian groups with no odd order part. We also determine \tilde \sigma (G) for each group G with order less than 16. The groups with symmetric crosscap numbers 1 and 2 have been classified. We show here that there are no groups with \tilde\sigma=3; this affirms a conjecture of Tucker.
May, Coy L. The symmetric crosscap number of a group. Glasgow mathematical journal, Tome 43 (2001) no. 3, pp. 399-410. doi: 10.1017/S0017089501030038
@article{10_1017_S0017089501030038,
author = {May, Coy L.},
title = {The symmetric crosscap number of a group},
journal = {Glasgow mathematical journal},
pages = {399--410},
year = {2001},
volume = {43},
number = {3},
doi = {10.1017/S0017089501030038},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089501030038/}
}
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