New posts in Finite Groups

Does $p \mid \frac{|{\rm{Stab}}(Q)|}{|\bigcap_{P\in {\rm{Syl}}_p(G)}{\rm{Stab}}(P)|}, \space\forall Q \in \operatorname{Syl}_p(G)$?

Nonexistence of a simple group of order 576

Nonexistence of a simple group of order 420

Inner automorphisms of group algebras vs. inner automorphisms of the group

Show that the number of nonisomorphic finite groups of order $n$ is at most $n^{n^2}.$

Let $n, k\in\Bbb{N},n\ge 2, k\ge 2$ and $(G,\cdot)$ be of order $n$. Prove $(n,k)=1 \iff$ for all $H\le G$ we have $H=\{x\in G \mid x^k\in H\}$

Torsion in abelian groups

Equivalent definitions of a $p$-group

Does $\alpha=\beta f \Rightarrow f$ isomorphism?

Number of ways to label die with opposing faces summing to 7