New posts in P Groups

Is every direct product of (finite) cyclic groups abelian?

Abelian finite groups and their subgroups

Let $G$ be a nonabelian group of order $p^{3},$ where $p$ is a prime. Show that $G$ has exactly $p^{2}+p-1$ distinct conjugacy classes.

Equivalent definitions of a $p$-group

$p$-groups in which the centralizers are normal

infinite abelian group where all elements have order 1, 2, or 4

Prove, that group of order $p^2$ is abelian.

Is this Galois theory proof of Fundamental Theorem of Algebra correct?

In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.

Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$