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Facts About Group Theory

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Please help with the following problem.

Give 5 interesting facts about group theory (or tensor calculus). Each one need only be 1 to just a few sentences - please list separately and under each fact provide any links to websites or pictures etc. These facts need not be anything original.

Thank you for your time and input.

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This solution helps with facts about group theory. It gives 5 interesting facts about group theory. The explanation is given 355 words.

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See the attachment. I tried to cover various topics of group theory. I can provide thousands of interesting facts from group theory.

Every group of order n is isomorphic to a subgroup of the symmetric group S_n (Cayley's theorem). Recall that the symmetric group S_n is defined as a set of all permutations on the first n integers, where the multiplication of permutations is given by their compositions. http://www-math.mit.edu/~dav/symmetricgroup.pdf

A group G of order n is cyclic if and only if for every divisor d of n the group G ...

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