Show that $G\neq\bigcup_{g\in G}gHg^{-1}$ for any $H\subsetneq G$
72150
Union of the conjugates of a proper subgroup
115606
Proofs involving $ (A\setminus B) \cup (A \cap B)$
107716
Show that $G$ is cyclic
122581
Prove or disprove that $G_1/H_1 \cong G_2/H_2$
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
86505
Let $A,B \subset \mathbb{R}$. Show that $\sup(A \cup B) = \max\{\sup A, \sup B\}$
48081
Prove that for all $n \in \mathbb{N}$: $2^{n-1}(a^n + b^n) \ge (a + b)^n$
38946
Show that $\{\cup_{n\in K} (n, n+1]: K \subset \mathbb{Z}\}$ is a $\sigma$-algebra on $\mathbb{R}$
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
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 $[G:N]=p$
19396
For subspaces, if $N\subseteq M_1\cup\cdots\cup M_k$, then $N\subseteq M_i$ for some $i$?
68918
Show that $A\cap B\subseteq A$ and $A\subseteq A\cup B$
4315
show that if $n\geq1$, $(1+{1\over n})^n<(1+{1\over n+1})^{n+1}$
95534
If $|G|=p^nq$, then $G$ contains a unique normal subgroup of index $q$
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
93596
If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.
141683
$ |G_1 |$ and $|G_2 | $ are coprime. Show that $K = H_1 \times H_2$