X-Nico

unusual facts about cyclic group


Rotation group

Cyclic group, rotational symmetry group for an object with n-fold symmetry in a plane of rotation


Minimal counterexample

The Feit–Thompson theorem, that infinite simple groups that are not cyclic groups have even order, was based on the hypothesis of some, and therefore some minimal, simple group G of odd order.


see also

Generic polynomial

Lenstra showed that a cyclic group does not have a generic polynomial if n is divisible by eight, and Smith explicitly constructs such a polynomial in case n is not divisible by eight.