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New posts in cyclic-groups
On the Factor group $\Bbb Q/\Bbb Z$ [duplicate]
abstract-algebra
group-theory
abelian-groups
cyclic-groups
Let $G$ be a finite Abelian group that has exactly one subgroup for each divisor of $|G|$. How does this imply that $G$ is cyclic? [duplicate]
group-theory
finite-groups
abelian-groups
cyclic-groups
Is $\mathbb{Z}^2$ cyclic?
abstract-algebra
group-theory
abelian-groups
cyclic-groups
Find the number of homomorphisms between cyclic groups.
abstract-algebra
group-theory
finite-groups
cyclic-groups
Any group of order $n$ satisfying $\gcd (n, \varphi(n)) =1$ is cyclic
abstract-algebra
finite-groups
cyclic-groups
totient-function
Find all homomorphisms $\varphi : \Bbb Z_6 \to S_3$. [duplicate]
group-theory
symmetric-groups
cyclic-groups
Why is the set of integers with the operation of addition considered a cyclic group?
group-theory
cyclic-groups
integers
if $G$ only has one subgroup of order $p$ and one subgroup of order $q$, then $G$ is a cyclic group
group-theory
cyclic-groups
Is $(\mathbb{Q^+},\cdot)$ cyclic?
abstract-algebra
group-theory
cyclic-groups
Find all proper nontrivial subgroups of $\mathbb Z_2 \times \mathbb Z_2 \times \mathbb Z_2$ - Fraleigh p. 110 Exercise 11.10
group-theory
solution-verification
cyclic-groups
If $G$ is cyclic then $G/H$ is cyclic?
abstract-algebra
group-theory
cyclic-groups
quotient-group
Cyclicness of a quotient of subgroups of infinite cyclic group
abstract-algebra
group-theory
symmetric-groups
cyclic-groups
quotient-group
How to prove that $\mathbb{C}_n$ is a subgroup of $(\Bbb C\setminus\{0\},\cdot)$. [closed]
group-theory
cyclic-groups
Cyclic Automorphism group
abstract-algebra
group-theory
cyclic-groups
automorphism-group
Does every group have a 'cyclization'?
abstract-algebra
group-theory
cyclic-groups
When is the automorphism group $\text{Aut }G$ cyclic?
group-theory
finite-groups
abelian-groups
cyclic-groups
Help to prove that $ U_{p} $ is a cyclic group.
abstract-algebra
group-theory
finite-groups
cyclic-groups
totient-function
Group $G$ is cyclic $\iff$ every subgroup of $G$ has the form $G^k$, where $G^k=\{g^k\mid g\in G\}$
abstract-algebra
group-theory
cyclic-groups
Describe all of the homomorphisms from $\Bbb Z_{24}$ to $\Bbb Z_{18}$. [duplicate]
group-theory
finite-groups
cyclic-groups
group-homomorphism
Prove that a cyclic group with only one generator can have at most 2 elements
abstract-algebra
gcd-and-lcm
cyclic-groups
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