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Existence proofs
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How to find groups with given properties
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New groups from old
How to find groups with given properties
To show that a group element is non-trivial, show that it has a non-trivial action or image
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Littlewood-Paley heuristic for derivative
Geometric view of Hölder's inequality
Diagonal arguments
Finding an interval for rational numbers with a high denominator
Try to prove a stronger result
Use self-similarity to get a limit from an inferior or superior limit.
Prove a consequence first
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