For subgroups $H_{1,2,3} \lneq G$ so that $\bigcup\limits_{i=1}^3H_i = G$ show: $[G : H_i]=2$
124237
Group equals union of three subgroups
136083
Show that $\sigma\circ\phi : G_1 \to G_3$ is an isomorphism
39165
Suppose $G$ is a group and $H,K \trianglelefteq G$. If $H \cap K =1$ the $hk=kh$ for all $k \in K, h \in H$?
65744
How can I Prove that H=G or K=G
28722
Prove that $H$ is a abelian subgroup of odd order
103002
Group equals union of two subgroups
128652
Subgroups of $\mathbb Z \times(\mathbb Z/n\mathbb Z)$
93596
If $H\leq G$ and $[G:H]=2$, then $H$ is normal in $G$.
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
150042
Prove $x^{-1}Hx$ is a subgroup of $G$
156319
Show that a group with $|G| = 33$ contains an element of order $3$
7575
Show the commutator subgroup of $S_{n}$ is $A_{n}$ for $n \geq 5$
151621
$G$ a group and $H, K\mathrel{\unlhd}G$. Assuming that $H \cap K = \{1_G\}$ and $G = \langle H, K \rangle$, prove that $G \cong H \times K$
127720
Prove that $\bigcup_{n \in \Bbb{N}} [1/n,1] = (0,1]$.
107935
If $G$ is a group, $H$ is a subgroup of $G$ and $g\in G$, is it possible that $gHg^{-1} \subset H$?
140334
Let $G$ be a group and $H$ be a subgroup of $G$ of index $2$ .Then show that if $a,b\notin H$ then $ab\in H$.
33945
Showing that $|N \cap Z(G)| > 1$ for normal subgroups of p-groups