Proper symmetry group/Fix/Finite subgroup/Numerical properties/Exercise

Consider the proof zu fact with the notation used there. Justify the following statements.

a) A proper isometry with two fixed axes is the identity.

b) ${}G$ is the union of all ${}G_{H}$.

c) Let ${}g\neq \operatorname {Id}$. The element ${}g$ appears in exactly two ${}G_{H}$. In which?

d) The class of semiaxes ${}K_{i}$ contains ${}n/n_{i}$ elements.

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