Prove - intersection of subgroups is a subgroup.
39469
If $P \leq G$, $Q\leq G$, are $P\cap Q$ and $P\cup Q$ subgroups of $G$?
138297
Let $G = GL_2\mathbb (R)$. Show that $T$ is a subgroup of $G$
43310
Proving $A\cap(B-C)$ is equal to $(A\cap B)-(A\cap C)$
144788
Cosets of a subgroup do not overlap
99346
Prove a result on transitive group actions.
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 $ab\in H$.
13453
Bijection map from a set of subgroup to another set of subgroup under some condition.
24181
Showing that $G$ is a group under an alternative operation.
117414
How would I prove what elements $S_3$ contains, and what its subgroups are?
98739
If $H$ is a subgroup of $G$ and $K$ is a subgroup of $H$, then $$|G:K|=|G:H||H:K|$$
52105
Prove that $HK$ is a subgroup iff $HK=KH$.
74311
Proving that the Intersection of any Collection of Compact Sets is Compact
102859
Proving that $G$ is a group if $a*x=b$ and $y*a=b$ have solutions.
156941
Subgroups of $\mathbb{Z}$
42891
Prove that $Z(G)$ which is the center of $G$ is a subgroup of $G$
85508
Prove that $G$ is an abelian group if $\{(g, g):g\in G\}$ is a normal subgroup.
26766
Proving : $A \cap (B-C) = (A \cap B) - (A \cap C)$