Prove group G has a subgroup $H_i$ where group operation is multiplication
106277
Prove that $G$ contains a subgroup $H_i$ for each $i\in\Bbb Z$ with $\dots\subset H_{−2}\subset H_{−1}\subset H_0\subset H_1\subset\dots?$
46863
Show that $g$ is injective
103002
Group equals union of two subgroups
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
124237
Group equals union of three subgroups
114522
Prove that identity is unique in a group
5042
Order of a product of subgroups. Prove that $o(HK) = \frac{o(H)o(K)}{o(H \cap K)}$.
106927
How do I prove $[G:H\cap K]\leq [G:H][G:K]$?
30676
$G'$ and the product of all the elements in an odd order group
129485
A subgroup of a cyclic group is cyclic - Understanding Proof
67919
Subgroup of the unit circle under complex multiplication
132127
Proving a direct product of groups is a group
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
106779
How to show if $H,K$ are normal subgroups in a group $G$ then $[H,K] \leq H \cap K$
71420
Prove that a group is abelian.
28722
Prove that $H$ is a abelian subgroup of odd order
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$