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Infinite cyclic group
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Mathematics
Area of mathematics
Algebra
Group theory
Group
Cyclic group
2026-09-24
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An infinite
cyclic group
is generated by an element of
infinite order
and is isomorphic to the
additive group
of
integers
.
Ancestors
(7)
Cyclic group
Group
Group theory
Algebra
Area of mathematics
Mathematics
Home
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(19)
Augmentation ideal of the infinite cyclic group
Cayley graphs of the integers
Cyclic group
Finitely generated subgroup of the rational additive group
Fundamental group
Group
Infinite line as a Cayley graph
Past exam of the mathematics course of the University of Cambridge
/
2003
/
iii
/
Paper 28
/
3
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2005
/
iii
/
Paper 17
/
3
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2014
/
ia
/
Paper 3
/
1D
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2014
/
iii
/
Paper 4
/
3
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2014
/
iii
/
Paper 4
/
4
/
i
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2017
/
iii
/
Paper 133
/
3
/
b
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2019
/
iii
/
Paper 143
/
2
/
a
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2019
/
iii
/
Paper 149
/
1
/
b
/
Solution
Past exam of the mathematics course of the University of Cambridge
/
2024
/
iii
/
Paper 133
/
1
/
c
/
Solution
Poly-infinite cyclic group
Trefoil knot
Unknot
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