Let $G$ be a group of order $8$ and $y$ be an element of $G$ of order $4$. Prove that $y^2 \in Z(G)$
127603
If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$
15210
Group of order 6 proof
65972
Show that a group of order $108$ has a normal subgroup of order $9$ or $27$.
88718
A group is generated by two elements of order $2$ is infinite and non-abelian
13631
Showing group with $p^2$ elements is Abelian
22632
Galois group of $x^4-2$
84789
Order of products of elements in a finite Abelian group
74586
Prove that every group of order $4$ is abelian
85579
$G$ a group s.t. every non-identity element has order 2. If $G$ is finite, prove $|G| = 2^n$ and $G \simeq C_2 \times C_2 \times\cdots\times C_2$
121423
Prove that every element of a finite group has an order
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
13355
Product of elements of a finite abelian group
18881
Number of elements of order $7$ in a group
81543
Finite abelian group contains an element with order equal to the lcm of the orders of its elements
60208
Proof of property of abelian group
112974
The $h-$th power of every element in a finite group of order $h$ is the identity element of the group
64518
Prove $S_4$ has only 1 subgroup of order 12