Assertion: group | /r/HasAspect | a generator g
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Source sentences:
text: By definition, the group is cyclic if and only if it has a generator g (a generating set {g} of size one), that is, the powers g 0 , g 1 , g 2 , … , {\displaystyle g^{0},g^{1},g^{2},\dots ,} give all possible residues modulo n coprime to n (the first φ ( n ) {\displaystyle \varphi (n)} powers g 0 , … , g φ ( n ) − 1 {\displaystyle g^{0},\dots ,g^{\varphi (n)-1}} give each exactly once).