Abstract Alg, Lec 17A: Abstract Nonsense :-), Apps of Group Theory, 'Products' & Ext Direct Products

(0:00) Lecture plan.
(0:45) Abstract nonsense is an "official term" with its own Wikipedia page.
(3:10) Real life applications of group theory.
(6:29) Rotation group of a soccer ball (football) using the Orbit-Stabilizer theorem (mention crystallography and buckyballs as well).
(12:18) My experience with soccer as a kid.
(13:37) The number of elements in the "product" of two subgroups and a proof that a group of order 18 can have at most one subgroup of order 9.
(19:47) HK is not necessarily a subgroup of G and given an example.
(21:35) External direct product definition.
(24:35) Order of an external direct product of finitely many finite groups and the order of an element in such a group (& basketball story).
(26:48) Example: the external direct product of Z4 with itself (it is a non-cyclic Abelian group of order 16). How many elements does it have of each possible order?

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