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References to 'generator'
1. $GL_2(\mathbb{Z})$ by rm50
2. a finite ring is cyclic if and only its order and characteristic are equal by mathcam
3. A finitely generated group has only finitely many subgroups of a given index by avf
4. abelian group is divisible if and only if it is an injective object by joking
5. additive form of Hilbert's theorem 90 by mathwizard
6. automorphism group of a cyclic group by rm50
7. behavior by Wkbj79
8. behavior exists uniquely (finite case) by Wkbj79
9. behavior exists uniquely (infinite case) by Wkbj79
10. conductor of a vector by CWoo
11. criteria for cyclic rings to be isomorphic by Wkbj79
12. criterion for cyclic rings to be principal ideal rings by Wkbj79
13. cyclic group by yark
14. cyclic ring by Wkbj79
15. cyclic rings and zero rings by Wkbj79
16. cyclic rings of behavior one by Wkbj79
17. cyclic rings that are isomorphic to $k\mathbb{Z}$ by Wkbj79
18. example of a non-fully invariant subgroup by Algeboy
19. example of groups of order pq by jh
20. example of Schreier's Lemma by Algeboy
21. examples of semidirect products of groups by rm50
22. finding the order of a group by Algeboy
23. free product with amalgamated subgroup by mathcam
24. generalized dihedral group by yark
25. groups of order pq by yark
26. groups with abelian inner automorphism group by rm50
27. Hilbert Theorem 90 by djao
28. Kolakoski sequence by PrimeFan
29. Minkowski's theorem by alozano
30. mock-up of scientific calculator by PrimeFan
31. nonabelian group by drini
32. nonprincipal real characters $\mod p$ are unique by rm50
33. primitive root by CWoo
34. proof of fundamental theorem of finitely generated abelian groups by puuhikki
35. proof of Hilbert Theorem 90 by mathcam
36. proof of Kummer theory by rm50
37. proof of the converse of Lagrange's theorem for finite cyclic groups by Wkbj79
38. proof that all cyclic groups are abelian by Wkbj79
39. proof that all cyclic groups of the same order are isomorphic to each other by Wkbj79
40. proof that all subgroups of a cyclic group are cyclic by Wkbj79
41. proof that every subring of a cyclic ring is an ideal by Wkbj79
42. rings whose every module is free by joking
43. root system underlying a semi-simple Lie algebra by rmilson
44. Schreier's lemma by Algeboy
45. straight-line program by Algeboy
46. subgroups of finite cyclic group by pahio
47. subsemigroup of a cyclic semigroup by CWoo
48. supersymmetry by bci1
49. the multiplicative identity of a cyclic ring must be a generator by Wkbj79
50. Thue system by CWoo
51. Ulrich module by yshen
52. variety of groups by yark
53. Weyl algebra by GrafZahl