Prove that a finite p-group G is simple if and only if its order is p.
67973
Prove that a finite abelian group is simple if and only if its order is prime.
150760
Are there any distinct finite simple groups with the same order?
125640
Group of order $p^2$ is abelian.
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
113357
Groups of order $pqr$ and their normal subgroups
6115
Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
8746
Groups of order $pq$ without using Sylow theorems
64269
Finding the minimal $n$ such that a given finite group $G$ is a subgroup of $S_n$
43580
Let $p$ be a prime number and $G$ a non abelian group or order $p^3$. Prove that $Z(G) = [G,G]$.
110708
On proving that a finitely generated group has a finite number of subgroups with index $n$.
79995
G is group of order pq, pq are primes
21673
If $|G| = p^n$ then $G$ has a subgroup of order $p^m$ for all $0\le m <n.$
43059
Show that $g^k=e$ if and only if the order of $g$ is finite and divides $k$.
121481
Non-abelian finite $p$-group in which every element has prime order?
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
85579
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
3213
There exists only two groups of order $p^2$ up to isomorphism.