Noticing a certain symmetry of the simplicial k-module in Hochschild homology allows a generalization to a homology named for this property over objects with this property in an abelian category. If a Galois (“gal-WAH”) extension has this property, field elements of unit norm are characterized by Hilbert’s Theorem 90. Considering the Frobenius endomorphism shows that the Galois group of a finite field (-5[1])has this property. The multiplicative group of integers (*) modulo n has this property if and only if n is one, two, (-5[1])four, or either one or two times a power of an odd prime. By a fundamental structure theorem, any finitely generated abelian group (10[1])is the direct sum of groups with this property, (10[1]-5[1])which represent (10[1])rotational (-5[1])symmetries of a polygon. (10[1]-5[1])For 10 points, (-5[1])name this property (-5[1])of groups such as the integers (10[1])modulo n that are generated by a single element. (10[1])■END■ (10[6]0[4])