Let p be an odd prime number, and let n be a positive integer divisible by p. Show that $D_n$ has only one p-Sylow subgroup
29736
Sylow Subgroups of a Dihedral Group
108830
Let $G$ be a group of order $2p$ , where $p$ is a prime greater than $2$. Then, G is isomorphic to $\mathbb{Z}_{2p}$ or $D_p$
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
99205
Group of order $p^k q$ where $p$ and $q$ are distinct primes - how to prove this property?
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
61235
Sylow $p$-subgroup of a direct product is product of Sylow $p$-subgroups of factors
40513
A finite group which has a unique subgroup of order $d$ for each $d\mid n$.
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
70066
Show that product of primes, $\prod_{k=1}^{\pi(n)} p_k < 4^n$
44019
Show that for any prime $ p $, there are integers $ x $ and $ y $ such that $ p|(x^{2} + y^{2} + 1) $.
103423
Normal subgroup where G has order prime
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
61546
Prove that for each prime $p$ there exists a nonabelian group of order $p^3$
19458
Finite groups and Normal subgroups - $G$ is a finite group such that $|G|=n$. Let $p$ be the smallest prime such that $p|n$.
54453
Finite abelian $p$-group with only one subgroup size $p$ is cyclic
111375
Normality of subgroups and Sylow groups under homomorphisms...