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New posts in cyclic-groups
Are cyclic groups always abelian? [closed]
abstract-algebra
group-theory
intuition
abelian-groups
cyclic-groups
A subgroup of a cyclic group is cyclic - Understanding Proof
abstract-algebra
group-theory
cyclic-groups
If $H$ is a cyclic subgroup of $G$ and $H$ is normal in $G$, then every subgoup of $H$ is normal in $G$.
abstract-algebra
group-theory
cyclic-groups
normal-subgroups
Is the cyclic group $\langle x\rangle$ always a subgroup of $G$ for any $x\in G$?
group-theory
solution-verification
cyclic-groups
finitely-generated
Show that if $ab$ has finite order $n$, then $ba$ also has order $n$. - Fraleigh p. 47 6.46.
group-theory
finite-groups
cyclic-groups
A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
abstract-algebra
group-theory
finite-groups
cyclic-groups
Finite groups with exactly one maximal subgroup
abstract-algebra
group-theory
finite-groups
cyclic-groups
Order of automorphism group of cyclic group [closed]
abstract-algebra
group-theory
cyclic-groups
automorphism-group
Let $G$ be an abelian group of order $pq$ with $gcd(p,q)=1$. Show that $G$ is cyclic.
group-theory
cyclic-groups
How can this subgroup $H$ of a cyclic group $G=\langle x \rangle$ contain the identity element if $H= \{1x, 2x, 3x, .... \} $?
abstract-algebra
group-theory
soft-question
cyclic-groups
Number of homomorphisms between two cyclic groups.
group-theory
finite-groups
cyclic-groups
group-homomorphism
Confusion about the last step of this proof of " Every subgroup of a cyclic group is cyclic":does not subcase $2.2$ contradict the desired conclusion
abstract-algebra
group-theory
soft-question
cyclic-groups
Let $G$ be a abelian group such that $|G| = 2p$ and $p$ Is a odd prime number. Prove $G$ is a cyclic group. [duplicate]
group-theory
abelian-groups
cyclic-groups
Why must a field whose a group of units is cyclic be finite?
abstract-algebra
group-theory
field-theory
finite-fields
cyclic-groups
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\Bbb{Z}_{2p}$ and $D_p$ for prime $p>2$.
group-theory
finite-groups
cyclic-groups
group-isomorphism
dihedral-groups
Product of two cyclic groups is cyclic iff their orders are co-prime
abstract-algebra
group-theory
elementary-number-theory
cyclic-groups
How to find a generator of a cyclic group?
abstract-algebra
group-theory
cyclic-groups
Groups of order $pq$ without using Sylow theorems
group-theory
cyclic-groups
Subgroups of a cyclic group and their order.
abstract-algebra
group-theory
cyclic-groups
For what $n$ is $U_n$ cyclic?
abstract-algebra
group-theory
cyclic-groups
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