Show that if G is a group with $G = p ^ n$
69820
A nontrivial p-group has nontrivial center
156319
Show that a group with $|G| = 33$ contains an element of order $3$
13834
Show that G is a group, if G is finite, the operation is associative, and cancellation law holds
75127
Group $G$ of order $p^2$: $\;G\cong \mathbb Z_{p^2}$ or $G\cong \mathbb Z_p \times \mathbb Z_p$
13631
Showing group with $p^2$ elements is Abelian
133001
$G$ simple group and there exists a subgroup of index $n$. Show that: $|G|$ divides $n!/2$
41237
$H$ is normal subgroup of $G$ iff $gHg^{-1}=H$ for every $g$ of $G$
50706
$|G|=p(p+1)$ for $p$ prime, then $G$ has a normal subgroup of order $p$ or $p+1$
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$
131204
A non-trivial normal subgroup N of a finite group G or order $p^n$ is such that $N\cap Z(G)\neq \{ 1\}$
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
46863
Show that $g$ is injective
61550
Existence of elements of order $p^k$ in a finite group
79452
How to prove that it is a group?
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 $G$.
42389
If $(G, \oplus)$ has order $2n$, prove that every proper subgroup of $(G, \oplus)$
46355
If $[G:H]=n$, is it true that $x^n\in H$ for all $x\in G$?