In algebra, a
cyclic group or
monogenous group is a
group that is
generated by a single element. That is, it consists of a set of elements with a single invertible
associative operation, and it contains an element
g such that every other element of the group may be obtained by repeatedly applying the group operation or its inverse to
g. Each element can be written as a power of
g in multiplicative notation, or as a multiple of
g in additive notation. This element
g is called a
generator of the group.