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Cyclic group

In abstract algebra, a cyclic group or monogenous group is a group, denoted Cn (also frequently Z {\displaystyle \mathbb {Z} } n or Zn, not to be confused with the commutative ring of p-adic numbers), that is generated by a single element. That is, it is a set of invertible elements with a single associative binary operation, and it contains an element g…

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Subgroups

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Cyclic group

Nodes133
Edges132
Triples214
Avg. degree1.99
Density0.015038
Components1

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Cyclic group

Top relations

related to References · 127
Cyclic group → Algebra, Alonso, Alpha Science, Amer, American Mathematical Monthly, American Mathematical Society, An Introduction, Anna University, Applications, Applied Mathematics, Balakrishnan, Bernd, Brian, Business Media, Cambridge, Cambridge University Press, Caroline, Categorical Algebra, Cayley, Cengage Learning
related to Modular multiplication · 13
Cyclic group → A033948, Euler, For, In, Klein, More, OEIS, This, When, Z/6Z, Z/8Z, Z/nZ, Z/pZ
related to Galois theory · 9
Cyclic group → An, Conversely, For, Frobenius, Galois, Kummer, The, The Galois, Z/nZ
related to Subgroups · 9
Cyclic group → All, For, Specifically, The, There, Thus, Z/0Z, Z/nZ, Z/pZ
related to Additional properties · 7
Cyclic group → Every, For, Lagrange's, That, The, This, Z/p
related to External links · 7
Cyclic group → CourseNotes/gt, Cyclic, Eric, Group, GroupNamesEvery, MathWorld, Milne
related to Integer and modular addition · 7
Cyclic group → Euler, Every, For, In, It, The, Z/nZ
related to Cayley graph · 6
Cyclic group → Cayley, However, In, The Cayley, These, They
related to Rotational symmetries · 5
Cyclic group → If, In, S1, The, Z/nZ
related to Virtually cyclic groups · 5
Cyclic group → An, Every, Gromov, In, Z/nZ

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Important terminology

group cyclic order groups isomorphic finite every nz prime element subgroup isbn integers number theory generated subgroups set elements single

Entity relationships Subject–Predicate–Object triples

SubjectPredicateObjectConfidenceSrc
Cyclic groupis aabelian group0.90text
Cyclic groupis agroup which is equal to one of its cyclic subgroups0.90text
Cyclic groupis acritical base case for the representation theory of more general finite groups0.90text
Cyclic groupis agroup in which each finitely generated subgroup is cyclic0.90text
15instance ofbut some are composite0.80text
Cyclic grouprelated to Additional propertiesEvery0.60section
Cyclic grouprelated to Additional propertiesThat0.60section
Cyclic grouprelated to Additional propertiesThis0.60section
Cyclic grouprelated to Additional propertiesFor0.60section
Cyclic grouprelated to Additional propertiesLagrange's0.60section
Cyclic grouprelated to Additional propertiesZ/p0.60section
Cyclic grouprelated to Additional propertiesThe0.60section

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