*in which we find out about permutation properties of Möbius maps and start looking at cross-ratios.
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# Groups

# Groups Lecture 21

*in which we view Möbius maps via matrices, and compose geometrically meaningful maps.
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# Groups Lecture 20

*in which we meet the unitary group and start exploring Möbius maps as transformations of the Riemann sphere.
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# Groups Lecture 19

*in which meet the orthogonal group and we rotate and reflect in two and three dimensions.
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# Groups Lecture 18

*in which we meet the quaternions, start exploring matrix groups and act with matrices on vectors and on matrices.
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# Groups Lecture 17

*in which we explore conjugacy classes in and , and prove that is simple.
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# Groups Lecture 16

*in which we learn about the symmetry groups of polyhedra, and start exploring conjugacy classes in the symmetric groups .
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# Groups Lecture 15

*in which we use actions to find sizes of groups, subgroups and stabilisers, and prove Cauchy’s Theorem.
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# Groups Lecture 14

*in which we meet several standard actions and prove Cayley’s Theorem.
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# Groups Lecture 13

*in which we meet orbits and stabilisers and prove the Orbit-Stabiliser Theorem.
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