Help, how can I show that [G: M] is finite and prime.
48273
If a maximal subgroup is normal, it has prime index
13734
Show that every group of prime order is cyclic
48585
Proving that if $G/Z(G)$ is cyclic, then $G$ is abelian
6115
Show that $GL_n(\mathbb{F})$ is a finite group iff $\mathbb{F}$ has a finite number of elements
123847
Cardinality of $GL_n(K)$ when $K$ is finite
90889
Prime ideals in a finite direct product of rings
344
Prove that if $p\in \mathbb{Z}$ is irreducible, then it is also prime.
126893
A group of order 2p (p prime) and other conditions - prove abelian.
100605
let $G$ to be finite abelian group of order O(G), let n to be prime number and (O(G),n)=1 prove that $g=x^n$ for any $ x \in G$
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
67272
Deduce that if $G$ is a finite $p$-group, the number of subgroups of $G$ that are not normal is divisible by $p$
81864
Finite group of order $mn$ with $\gcd(m,n) = 1$ .
43645
Show that $G/H\cong S_3$
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
39843
Let $P$ be a prime. Show that $\exists$ $x \in \mathbb{N}$ such that $f(x) = p$ then $\exists$ $y \in \mathbb{N}$ such that $g(y) = p$
70066
Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$
157884
For any prime $p>3$ show that 3 divides $2p^2+1$