Is the group of all rotations of R^2 cyclic?

At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get our expert's

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions.

A community for students.

Is the group of all rotations of R^2 cyclic?

Mathematics
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.

Get this expert

answer on brainly

SEE EXPERT ANSWER

Get your free account and access expert answers to this and thousands of other questions

check http://math.stackexchange.com/questions/148111/proof-that-finite-group-of-rotations-of-plane-is-cyclic

Not the answer you are looking for?

Search for more explanations.

Ask your own question

Other answers:

Its not showing any solution or any hint..
let me just give you the proof : https://s3.amazonaws.com/upload.screenshot.co/73cd8e1818
What is the case when the group becomes infinite? In the question the finite or infinite case was not mentioned...
I 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
for 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
So in general it is not cyclic, we may conclude?
On 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.
Yes, not necessarily cyclic...

Not the answer you are looking for?

Search for more explanations.

Ask your own question