Prove that in any group $A_n$ = $S'_n$
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
139835
Every Finite Group is Isomorphic to a Subgroup of $A_n$
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
94571
How can we prove that $N_G(H)=H$ implies $N_{f(G)}(f(H))=f(H)$
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
70394
Prove that $a * b$ is a group (Hungerford, 2nd ed., sec $7.2$, Exercise $22$)
65900
Show that a finite group with certain automorphism is abelian
118471
Prove that $1-\sum_{i=1}^n a_i < \prod_{i=1}^n(1-a_i) $
131594
Can the symmetric group $S_n$ be imbedded as a subgroup in $A_{n+1}$?
147253
Prove for any $K \leq G$, either $K \leq N$ or $KN=G$ and $[K:K \cap N]=p$ where N is normal in G and $[G:N]=p$
128834
Proving the number of even and odd permutations of a subgroup $H<S_{n}$ are equal, provided $H$ is not contained in $A_{n}$
150199
How to prove for a finite group that $|\langle g \rangle|=o(g)$?
84198
Step in Proof of Cardinality of Product of two Groups
74586
Prove that every group of order $4$ is abelian
97469
How to prove $|a^k|=n/\gcd(n,k)$ whenever $|a|=n$?
80601
Let $a,b$ be in a group $G$. Show $(ab)^n=a^nb^n$ $\forall n\in\mathbb{Z}$ if and only if $ab=ba$.
108310
$(a_1 a_2 \cdots a_n)^2=e$ in a finite abelian group