On the genus of a group

White, Arthur T.

doi:10.1090/S0002-9947-1972-0317980-2

On the genus of a group
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by Arthur T. White PDF

Trans. Amer. Math. Soc. 173 (1972), 203-214 Request permission

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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