Let G be a simple group and let ${n_p}$ be the number of Sylow p-subgroups, where p is prime. Show |G| divides $({n_p})!$.
139661
trouble applying Sylow's theorems
15526
Question on groups of order $pq$
140334
Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
97928
Normal subgroup of a normal subgroup
59007
Suppose $|G| = 105$. Show that it is abelian if it has a normal $3$-Sylow subgroup.
8746
Groups of order $pq$ without using Sylow theorems
123796
Order of automorphism group of a $p$-group is divisible by $p$.
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
72048
Finding Sylow 2-subgroups of the dihedral group $D_n$
44152
If $G$ has only one subgroup of order $n$, then that Subgroup is Normal
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
51352
Subgroups of a finite abelian group
61235
Sylow $p$-subgroup of a direct product is product of Sylow $p$-subgroups of factors
29802
Part of simple proof of nontrivial center in p-group
105139
Verification of Proof that a nonabelian group G of order pq where p and q are primes has a trivial center