# 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

July 23rd, 2022

July 30th, 2022

## Give an example of a nonabelian group such that G/Z(G) is...

November 17th, 2020

## Prove if any group has order 9, then it is abelian.

September 20th, 2020

## How can you tell whether two groups are homomorphic/isomorphic?

November 3rd, 2020

August 1st, 2022

June 19th, 2020

## 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

## |ab|=lcm(|a|,|b|) in an abelian group

October 10th, 2020

## Let G be a non-Abelian group with 8 elements

September 27th, 2020

June 5th, 2020

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

August 1st, 2022

## Finding all subgroups of Direct product of groups

October 8th, 2020

March 8th, 2020

August 1st, 2022

August 1st, 2022

March 9th, 2020

March 18th, 2020

March 26th, 2021

## The homomorphic image of an abelian group is abelian

November 24th, 2020

March 29th, 2021

## 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

## Example of an infinite abelian group having a non-cyclic finite subgroup

February 25th, 2020

August 1st, 2022

April 27th, 2020