Proving that ${\rm Aut}(G)=\{{\rm id}\} \implies |G| \in \{1,2\}$.
52121
Let $G$ be a finite group with $|G|>2$. Prove that ${\rm Aut}(G)$ contains at least two elements.
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
90332
Prove that that $U(n)$ is an abelian group.
151559
Please help: How to show that Aut(G) is a subgroup of Sym(G)
34929
Prove ${M}\choose{N_1}$ ${M}\choose{N_2}$ $\leq$ ${2M}\choose{N_1+N_2}$ for $M, N_1, N_2 \in \mathbb{N},\,M\geq N_1,N_2$.
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
53266
Show that $R/I\otimes_R R/J\cong R/(I+J)$
99346
Prove a result on transitive group actions.
83475
Prove Or Disprove: tr(AB)=tr(A)*tr(B)
76694
Proving that $UT=TU$ iff $U=g(T)$ for some polynomial $g$
99662
proving than every $2\times 2$ is similar to a united form
76863
How to show $ \sup \inf g(x,y) \leq \inf \sup g(x,y)$?
46106
Prove that $D_r \circ D_s = \{ (x,y) \in \mathbb{R}^2 \ | \ |x-y|<r+s \}$, where $D_a = \{ (x,y) \in \mathbb{R}^2\ | \ |x-y| < a \}$
60208
Proof of property of abelian group
78463
Prove that $\sup \{-x \mid x \in A\} = -\inf\{x\mid x \in A\}$
8374
How to prove that $R/I \otimes_R M \cong M / IM$
40321
$\operatorname{Aut}(\mathbb Z_n)$ is isomorphic to $U_n$.