Can someone please read the attached file and tell me his ideas? I want to be sure I understand the action of the Klein Four group....Is my interpretation correct?(adsbygoogle = window.adsbygoogle || []).push({});

I have some problem though. The Klein Four group has 4 elements, and it is able to describe the reflective symmetries of a square (as I interpreted it).

The dihedral group however, $D_2$ for example should be the same group right? (if I see the one $Z_2$ of the KF group as a cyclic group and the other $Z_2$ are reflection). $D_2$ however does not describe a square....

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# Klein Four Group's action

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