The geometry of four-dimensional conformal Minkowski space is defined by one of these according to the (*) Erlangen program.
Chevalley and Steinberg name extraordinary and twisted versions of these things, respectively. For the extension E/F, one example of these denoted Gal(E/F) can be given a Krull topology to be made into a profinite one of these.  Another example of these is the collection of polygon symmetries, known as the  dihedral ones of these structures.  The geometry of four-dimensional conformal Minkowski space is defined by one of these according to the (*) Erlangen program. The order of a substructure of one of these things divides the order of the parent structure according to Lagrange's theorem. The operation that defines this structure must satisfy the axioms of closure, associativity, identity, and invertibility.  For 10 points, name these algebraic structures where an operation combines two set elements into another element, one example of which is the set of integers under multiplication.
Chevalley and Steinberg name extraordinary and twisted versions of these things, respectively.
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