Everything about Cyclic Group totally explained
In
group theory, a
cyclic group or
monogenous group is a
group that can be
generated by a single element, in the sense that the group has an element
g (called a "
generator" of the group) such that, when written multiplicatively, every element of the group is a power of
g (a multiple of
g when the notation is additive).
Definition
A group
G is called cyclic if there exists an element
g in
G such that
G = <
g> =
C2.
Virtually cyclic groups
A group is called
virtually cyclic if it contains a cyclic subgroup of finite
index. It is known that a finitely generated
discrete group with exactly two
ends is virtually cyclic. Every abelian subgroup of a
Gromov hyperbolic group is virtually cyclic.
Further Information
Get more info on 'Cyclic Group'.
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