Prove a certain group $G\lesssim A_m$
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
85222
Direct sum of finitely-many non-abelian groups
58707
Prove Quotient Group Isomorphism
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
91774
Existence of group $G$ with $|G|>2$ and automorphism group of odd order
150958
Group theory question. If $m$ and $n$ are relatively prime, and $a$, $b$ belong to group and $a^m = b^m$ and $a^n = b^n$, how would one prove $a = b$?
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
131306
Prove that a group of order $2^5 \cdot 7^5$ is not simple
118898
Is there a simple way of proving that $\text{GL}_n(R) \not\cong \text{GL}_m(R)$?
31252
"Efficient version" of Cayley's Theorem in Group Theory
3203
Quotient group $\mathbb Z^n/\ \text{im}(A)$
145254
$G$ be a non-nilpotent and supersoluble finite group.
154398
Show that H is a subgroup of G
43645
Show that $G/H\cong S_3$
87766
Using Cayley's Theorem to find an isomorphic subgroup.
135701
An example of a group such that $G \cong G \times G$