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The group elements are generated by (g, 1, 1, ...), (1, g, 1, ... ), (1, 1, g, ...) ... that is have a form (g^i1, g^i2, ... ) where g^p = 1 for some p.

There is an edge between elements in the group where elements at some index have powers of g different by 1 modulo p, that is g^1 and g^2 have a bidirectional edge for p = 4, but g^1 and g^3 do not.

Does there always exist a Hamiltonian cycle in such a group? What kind of structure does it have?

Example

For g = 1 under addition modulo 2 (0, 0, ... 1, 0, 0, 0) generate vertices of a hypercube. So the question is if there is a Hamiltonian cycle in the hypercube.

iggy
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  • Wouldn't this be better on the math stackexchange? What's the programming connection? – DSM Jan 12 '15 at 00:05
  • @DSM Hamiltonian problem is more of a computer science problem. Plus there are many questions on Hamiltonian cycles here. I added an example to the question. – iggy Jan 12 '15 at 14:51

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