*in which we apply group theory to prove Fermat-Euler, and use Lagrange to help us find subgroups or determine what a small group must look like.*

# Groups Lecture 10

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*in which we apply group theory to prove Fermat-Euler, and use Lagrange to help us find subgroups or determine what a small group must look like.*

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*in which we finish the proof of Lagrange’s Theorem, see what consequences it has on orders of elements, and meet equivalence relations.
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*in which we show that the sign of a permutation is a surjective group homomorphism, and meet cosets.
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*in which we prove that disjoint cycle notation works and get a first glimpse of the sign of a permutation.
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*in which we meet the symmetric groups and their cycle notation.
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*in which we investigate cyclic groups, generators, dihedral groups and cartesian products of groups.
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*in which we learn more about group homomorphisms and meet images and kernels.
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