Explain why it is impossible for $G$ to have such Sylow $p$-subgroups
45254
Sylow Theorem Explanation
113925
Normal Subgroup Counterexample
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups
28181
Sylow subgroups of $S_3$ and $S_4$
47692
Homomorphic image of a Sylow p-subgroup is Sylow p-subgroup.
74218
Show that $S_n$ has no subgroup of index $t$ for $2 < t < n$
157841
Existence of a non-abelian group of order $p^n$.
61064
Finite index subgroup $G$ of $\mathbb{Z}_p$ is open.
47731
Intersection of all $p$-Sylow subgroups is normal
19720
A normal subgroup intersects the center of the $p$-group nontrivially
89382
In a group $G$ where $\exists!$ nontrivial, proper subgroup, show that $G$ is cyclic and $\lvert G\rvert=p^2$, for $p$ prime.
142938
Sylow 2-subgroups of the group $\mathrm{PSL}(2,q)$
103423
Normal subgroup where G has order prime
137931
Problem from "The Theory of Finite Groups" by Kurzweil and Stellmacher
98474
Show the existence of a certain subgroup of F2
22301
If $G$ has no proper subgroup, then $G$ is cyclic of prime order
68955
Characterising subgroups of Prüfer $p$-groups.