In algebra, a cyclic group is a group that is generated by a single element, in the sense that every element of the group can be written as a power of some particular element g in multiplicative notation, or as a multiple of g in additive notation. This element g is called a "generator" of the group. Any infinite cyclic group is isomorphic to Z, the integers with addition as the group operation. Any finite cyclic group of order n is isomorphic to Z/nZ, the integers modulo n with addition as the group operation.
Read more about Cyclic Group: Definition, Properties, Examples, Representation, Subgroups and Notation, Endomorphisms, Virtually Cyclic Groups
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“There is nothing in the world that I loathe more than group activity, that communal bath where the hairy and slippery mix in a multiplication of mediocrity.”
—Vladimir Nabokov (1899–1977)