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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the genus of a group


Author: Arthur T. White
Journal: Trans. Amer. Math. Soc. 173 (1972), 203-214
MSC: Primary 05C10
MathSciNet review: 0317980
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Abstract: The genus of a group is defined to be the minimum genus for any Cayley color graph of the group. All finite planar groups have been determined, but little is known about the genus of finite nonplanar groups. In this paper two families of toroidal groups are presented; the genus is calculated for certain abelian groups; and upper bounds are given for the genera of the symmetric and alternating groups and for some hamiltonian groups.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1972-0317980-2
PII: S 0002-9947(1972)0317980-2
Keywords: Graph, group, generators and relations, Cayley color graph of a group, imbedding, genus of a graph, genus of a group
Article copyright: © Copyright 1972 American Mathematical Society