Can some finite groups be well ordered in a "meaningful" way? I mean, it is clear that we can trivially find a bijection between $\{1,...,n\}$ and a finite group $G$ with $n$ elements, but I am interested in well ordering that are based on some scheme or pattern with respect to some group property (for example, it is immediate to well-order a cyclic group).
Are there methods to well order a finite group in a meaningful way?
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group-theory
soft-question
finite-groups
order-theory
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5How is it immediate to well-order a cyclic group? If you mean the ordering "identity, generator, square of generator, ...", then which of the many generators will you choose? – 2012-06-07
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0You can obtain $n-1$ different wos, isn't it? – 2012-06-07
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3Other than the trivial group, there is no well-ordering on any finite group in a way that makes the group operation order-preserving. (Obvious.) – 2012-06-07