G is finite group. Need to proof that exists natural k that $g^k = e$
121423
Prove that every element of a finite group has an order
1251
If $[G:K]$ is finite, then $[H:H \cap K] = [G:K]$ iff $G = HK$ (Hungerford Proposition 4.8, Proof)
29717
Not sure how to go about this group theory proof
26449
$|G|=24$ prove that $G$ is not simple
82037
Suppose $G$ is a group generated by elements $x$ and $y$ where $xy^2 = y^3x$ and $yx^3 = x^2y$ What can you prove about $G$?
139984
Please help me, Group Theory. Prove $b^{33}=e$.
49768
If Gal(K,Q) is abelian then |Gal(K,Q)|=n
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
56650
Prove that $(G, \circ)$ is a group if $a\circ x = b$ and $x\circ a = b$ have unique solutions
105671
Let $g_n= {2^2}^n +1 $. Prove $g_0 · g_1 · · · g_{n−1} = g_{n} − 2$
37379
Let $G$ a group with normal subgroups $M,N$ such that $M\cap N=\{e\}$. Show that if $G$ is generated by $M\cup N$ then $G\cong M \times N$.
152741
Cardinal of a group $G$ such that for all $x\in G$ we have $x^2=e$
135188
Show that if $\vert G\vert = pq$, then either $G$ is abelian or $Z(G) = \{ e\}$.
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 $[G:N]=p$
36887
Suppose $G$ is a group of order 4. Show either $G$ is cyclic or $x^2=e$.
154878
Prove that $H$ is a normal subgroup in the finite group $G=\langle S\rangle $ iff $sHs^{-1}$ $\subseteq H$ for all $s\in S$.
84501
Proof involving Cyclic group, generator and GCD