Let $G$ be a group such that $|G| \ge 3$ then $|AutG| \ge 2$.
12455
$|G|>2$ implies $G$ has non trivial automorphism
158074
Cyclic group $G$ with generator $ab$.
26398
Group of even order contains an element of order 2
59561
Suppose that G is a group and N < G a normal subgroup. Prove G/N is simple
85011
Prove that $\exists a,g,h\in G\colon h=aga^{-1}, g\neq h ,gh=hg$ in a finite non-abelian group $G$.
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
92750
Groups where all elements are order 3
56245
Let H be a subgroup of a group G. Prove that the following statements are equivalent.
1364
Let $G$ be a group in which $a^2=e$ for all elements of $a$ of $G$. Show that $G$ is Abelian.
146760
Prove that H is a subgroup of G
111049
Groups with given automorphism groups
151699
Group of inner automorphisms of a group $G$
77221
Prove that $G$ has a subgroup isomorphic to $G/H$.
19458
Finite groups and Normal subgroups - $G$ is a finite group such that $|G|=n$. Let $p$ be the smallest prime such that $p|n$.
152603
Group isomorphic to its automorphism group
133627
If $\phi(g)=g^3$ is a homomorphism and $3 \nmid |G|$, $G$ is abelian.