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anonymous
 one year ago
Is the group of all rotations of R^2 cyclic?
anonymous
 one year ago
Is the group of all rotations of R^2 cyclic?

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Its not showing any solution or any hint..

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3let me just give you the proof : https://s3.amazonaws.com/upload.screenshot.co/73cd8e1818

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0What is the case when the group becomes infinite? In the question the finite or infinite case was not mentioned...

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3I think we must have a "minimum positive angle of rotation" in the group for it to be cyclic; for infinite groups, we cannot guarantee the existence of a minimum rotation element in the group. so, my hunch is that there may exist some infinite groups of plane rotations that are not cyclic

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3for example, consider the group of rotations with angles whose measures are real numbers then, its easy to see, since there is no minimum positive element, the previous proof using euclid theorem fails

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So in general it is not cyclic, we may conclude?

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3On the other hand, the infinite group of rotations with angles whose measures are "integers" is cyclic. because there exists a minimum positive rotation angle : "1" those two examples of infinite groups make me believe that some infinite groups of plane rotations are cyclic and some are not.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.3Yes, not necessarily cyclic...
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