Category:Cyclic Groups
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This category contains results about Cyclic Groups.
Definitions specific to this category can be found in Definitions/Cyclic Groups.
The group $G$ is cyclic if and only if every element of $G$ can be expressed as the power of one element of $G$:
- $\exists g \in G: \forall h \in G: h = g^n$
for some $n \in \Z$.
Subcategories
This category has the following 15 subcategories, out of 15 total.
C
- Cyclic Group is Abelian (3 P)
- Cyclic Group of Order 3 (5 P)
- Cyclic Group of Order 8 (2 P)
E
G
- Group of Order p q is Cyclic (4 P)
P
Q
S
Pages in category "Cyclic Groups"
The following 54 pages are in this category, out of 54 total.
A
C
E
F
G
- Generators of Additive Group of Integers
- Generators of Infinite Cyclic Group
- Group Direct Product of Cyclic Groups
- Group Direct Product of Cyclic Groups/Corollary
- Group Direct Product of Infinite Cyclic Groups
- Group of Order 15 is Cyclic Group
- Group of Order 35 is Cyclic Group
- Group of Order p q is Cyclic
- Group Presentation of Cyclic Group
- Group whose Order equals Order of Element is Cyclic
- Groups of Order 2p