New posts in Abstract Algebra

Does the categorical notion of a coequalizer coincide with the usual quotient objects considered in algebra?

Why is it that the congruence relations usually correspond to some type of subobject?

Finding the structure of a group without using sylows theorem.

Why is $x^4-3x^2+18$ irreducible over the $3$-adics?

Can an isomorphism of subgroups of a finite group always be extended to an automorphism on the group?

What is the smallest group containing all finite cyclic groups?

Can two fields that have monomorphism to each other not be isomorphic?

Is $H$ a subgroup of $\Gamma$?

If not associative, then what?

Let $G$ be a finite abelian group, and let $n$ divide $|G|$. Let $m$ be the number of solutions of $x^n=1$. Prove that $n\mid m$.