Assertion: abelian group's element | /r/HasProperty | generator
Facets:
value: for cyclic groups of order
type: OTHER
Source sentences:
text: Element (identity element) (generator) (generator)
text: Such an element a is called a generator or a primitive element of the group.
text: An abelian group A is finitely generated if it contains a finite set of elements (called generators)
text: Normally, a cyclic group is defined as a set of numbers generated by repeated use of an operator on a single element which is called the generator and is denoted by
text: A non-generating element of G is an element that can always be removed from a generating set; that is, an element a of G such that whenever X is a generating set of G containing a, X −{a} is also a generating set of G .
text: Element (identity element) (generator) (generator)
text: Element (identity element) (generator) (generator)
text: Element (identity element) (generator) (generator)
text: Element (identity element) (generator) (generator)
text: Element (identity element) (generator) (generator)
text: Elements of order 2, which are generators for cyclic groups of order 2, are termed involutions.
text: If G = ⟨S⟩, then we say that S generates G, and the elements in S are called generators or group generators.