Cyclic group
"Cyclic group" in a Sentence (3 examples)
1986, N. S. Gopalakrishnan, University Algebra, New Age International, 2nd Edition, page 22, Proposition 1.5.6. Any subgroup of an infinite cyclic group is also an infinite cyclic group.
If u#58;G#95;1#92;rightarrow#92;mathbb#123;Z#125;#47;m#92;mathbb#123;Z#125; and v#58;G#95;2#92;rightarrow#92;mathbb#123;Z#125;#47;m#92;mathbb#123;Z#125; are isomorphisms of two cyclic groups with #92;mathbb#123;Z#125;#47;m#92;mathbb#123;Z#125;, then v#123;-1#125;#92;circu#58;G#95;1#92;rightarrowG#95;2 is an isomorphism.
2003, Alexander Retakh (translator), Ėrnest Borisovich Vinberg, A Course in Algebra, [2001, Э. Б. Винберг, Курс алгебры, Factorial Press] American Mathematical Society, page 152, Cyclic groups are the simplest groups imaginable.