New posts in Sylow Theory

Intuition behind picking group actions and Sylow

Let $G$ be a group of order $24$ having no normal subgroups of order $3$. Show that $G$ has four subgroups of order $6$.

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

Does a group of order $400$ always have a subgroup of order $200$?

$G$ is a finite group s.t. $(ab)^p=a^pb^p$; $P$ is its $p$-Sylow subgroup. Then there exists $N \unlhd G$ such that $N \cap P = (e)$ and $NP=G$.

Does $A_{17}$ have a subgroup of index $3$?

Construct a nonabelian group of order 44

Sylow Subgroups and Conjugation