How to show that the centralizer formed by $g\in A\cap B$ where $A$ and $B$ are 3-Sylow subgroups contains $A$ and $B.$
118022
Show that a group of order $180$ is not simple.
29736
Sylow Subgroups of a Dihedral Group
117414
How would I prove what elements $S_3$ contains, and what its subgroups are?
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
12502
The center of a non-Abelian group of order 8
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
13742
Proving that a normal, abelian subgroup of G is in the center of G if |G/N| and |Aut(N)| are relatively prime.
90511
Commutator subgroup of a dihedral group.
113936
Showing that a finite abelian group has a subgroup of order m for each divisor m of n
47179
Prove that $[N, G']=1$ when $N$ is a nilpotent subgroup of a group $G$?
122970
A question on $p$-groups, and order of its commutator subgroup.
156319
Show that a group with $|G| = 33$ contains an element of order $3$
32735
If $ \langle G, \star \rangle $ is an abelian group, then for all $a, b \in G$, show that $(a \star b)^{n} = a^{n} \star b^{n}$.
115182
Centre of symmetric group algebra
88199
The commutator subgroup of a quotient in terms of the commutator subgroup and the kernel
58251
To show every sylow p-subgroup is normal in G
88759
Proofs of Sylow theorems