Show that $a^m$ is in $H$ for every $a$ in $G$
121587
Let $H$ be a normal subgroup of index $n$ in a group $G$. Show that for all $g \in G, g^n \in H$
145397
How to prove that for every $i$, $a_i = i$
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
147398
If every element of $H$ and $G/H$ is a square, then prove that so is every element of $G$.
111703
If $H \leq G$ and $[G:H]! \leq |G|$ then $G$ is not simple
94507
Given $G$ group and $H \le G$ such that $|G:H|=2$, how does $x^2 \in H$ for every $x \in G$?
110672
Is it true that $aH = bH$ iff $ab^{-1} \in H$
98765
Showing that $G/(H\cap K)\cong (G/H)\times (G/K)$
130455
If $H,K⊲G$ and $H∩K = \{1_G\}$, then all elements in $H$ commute with all elements in $K$
98542
Prove that $H$ is a subgroup of an abelian group $G$
55350
H is a subgroup of G and G' is a subgroup of H. Prove H is normal in G.
111886
Let $(G,•)$ be a group in which $(a•b)^3 = a^3•b^3$. Prove that $H=\{x^3 : x \in G\}$ is a normal subgroup of $G$.
64932
Show that $\lim_{x\to a^{+}} g(x) =g(a)$
64747
If $A^m=I$ then A is Diagonalizable
96133
Prove that $ m_{a} \geq m_{g} \geq m_{h} $ using strict inequalities unless $ a = b $.
141043
$H$ normal in $G$. Need $G$ contain a subgroup isomorphic to $G/H$
154398
Show that H is a subgroup of G