I want to visualize everything in Mathematics.Is there a way to visualize the theorem I stated above?Can it be represented graphically?I want to be very analytical in this topic.So please can anyone suggest a good visualization or a textbook that discusses such topics? I want a visualization for this particular theorem.
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1This should be covered by your previous question: Can the concepts of abstract algebra be visualized as in analysis? – xxxxxxxxx Jun 06 '19 at 17:57
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I want particularly this theorem to be visualized by some means. – Jun 06 '19 at 18:10
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Please punctuate properly. – jgon Jun 06 '19 at 18:13
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Sorry for the mistakes.Can you suggest a visualization for the above theorem? – Jun 06 '19 at 18:17
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You may be interested in answers to MSE questions 2487500 "How can I visualise groups in Group Theory". – Somos Jun 07 '19 at 11:12
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Here's a geometric description of finite cyclic groups:
A finite group is cyclic if and only if it is isomorphic to a finite group of rotations of the circle $S^1$.
For example, the cyclic group of order $6$ is isomorphic to the group of rotations of $S^1$ through the $6$ angles $\frac{2\pi}{i}$, $i=0,1,2,3,4,5$.
Once you believe that this description of finite cyclic groups is true, or once you go to the trouble of proving that it is true, then here's a very simple "visual" proof that every subgroup of a finite cyclic group is cyclic: every subgroup of a group of rotations of $S^1$ is also a group of rotations of $S^1$.
Lee Mosher
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