Categories
Tags
Abelian-groups
New post in Abelian-groups
Giving examples of some group $G$ and elements $g,h \in G$ where $(gh)^{n}\neq g^{n} h^{n}$.
December 7th, 2022
abstract-algebra
abelian-groups
group-theory
If G/N is cyclic, then G is abelian.
July 23rd, 2022
cyclic-groups
group-theory
abelian-groups
abstract-algebra
Two abelian groups with the same order are isomorphic?
July 30th, 2022
group-theory
abelian-groups
Give an example of a nonabelian group such that G/Z(G) is...
November 17th, 2020
abelian-groups
group-theory
abstract-algebra
Prove if any group has order 9, then it is abelian.
September 20th, 2020
finite-groups
abstract-algebra
abelian-groups
group-theory
How can you tell whether two groups are homomorphic/isomorphic?
November 3rd, 2020
abelian-groups
group-isomorphism
group-homomorphism
finite-groups
group-theory
Non-isomorphic abelian groups of order $19^5$
August 1st, 2022
abstract-algebra
group-theory
finite-groups
abelian-groups
How many subgroups or order 8 an abelian Group of order 72 can have
June 19th, 2020
group-theory
abelian-groups
abstract-algebra
Prove or disprove: If H is a normal subgroup of G such that H and G/H are abelian, then G is abelian.
January 18th, 2020
abelian-groups
normal-subgroups
group-theory
|ab|=lcm(|a|,|b|) in an abelian group
October 10th, 2020
abstract-algebra
abelian-groups
finite-groups
group-theory
least-common-multiple
Let G be a non-Abelian group with 8 elements
September 27th, 2020
group-theory
abelian-groups
group-isomorphism
Show that fiber products exist in the category of abelian groups.
June 5th, 2020
category-theory
abelian-groups
abstract-algebra
Classify the abelian groups of order 81, 144 and 216
August 1st, 2022
abelian-groups
group-theory
finite-groups
Is a congruence (equivalence) class modulo n a group?
August 1st, 2022
group-theory
equivalence-relations
abelian-groups
modular-arithmetic
abstract-algebra
Automorphism iff G is abelian
August 1st, 2022
abstract-algebra
abelian-groups
List all abelian groups that have order 81 and contain an element of order 27
August 1st, 2022
abstract-algebra
abelian-groups
Show there is no non-abelian group of order 9
August 1st, 2022
abstract-algebra
group-theory
finite-groups
abelian-groups
Finding all subgroups of Direct product of groups
October 8th, 2020
abstract-algebra
group-theory
finite-groups
abelian-groups
Let G be a finite Abelian group and let p be a prime that divides the order of G. Then G has an element of order p.
March 8th, 2020
abstract-algebra
abelian-groups
proof-explanation
group-theory
Prove or disprove that there is an abelian, noncyclic group of order 52.
August 1st, 2022
group-theory
abelian-groups
cyclic-groups
sylow-theory
Groups - Prove that if $G/Z(G)$ is cyclic then $G$ is abelian
August 1st, 2022
finite-groups
abelian-groups
cyclic-groups
$U_{14}$ and $U_{18}$ : why are they isomorphic to $\mathbb{Z}_2 \times \mathbb{Z}_3$?
March 9th, 2020
group-theory
abelian-groups
Abstract Algebra. Let $\mathit{G} $ be an abelian group. Show that the elements of finite order in $\mathit{G}$ form a subgroup of $\mathit{G}$.
March 18th, 2020
abstract-algebra
group-theory
abelian-groups
torsion-groups
Group of order $pq$. Show that there exist an element of order $p$ in G.
March 26th, 2021
abstract-algebra
group-theory
prime-numbers
finite-groups
abelian-groups
The homomorphic image of an abelian group is abelian
November 24th, 2020
abelian-groups
group-homomorphism
group-theory
Elementary divisors of a group
March 29th, 2021
abstract-algebra
abelian-groups
Show that if $H$ and $K$ are subgroups of one abelian group $G$, then $G_1=\{hk\mid h\in H\text{ and }k\in K\}$ is a subgroup of $G$
September 14th, 2021
abelian-groups
abstract-algebra
group-theory
Example of an infinite abelian group having a non-cyclic finite subgroup
February 25th, 2020
group-theory
finite-groups
abelian-groups
infinite-groups
Find all the subgroups of $\mathbb{Z}_7$ and $\mathbb{Z}_9^\times$
August 1st, 2022
abelian-groups
finite-groups
group-theory
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
April 27th, 2020
abelian-groups
←
1
2
3
4
5
6
7
8
9
…
12
13
→