If $G$ has more than one nontrivial elements with order 2, how to show that $\prod^n_{x=1}a_x=1$?
13355
Product of elements of a finite abelian group
117468
$o(g^{k})=\frac{o(g)}{\gcd(o(g),k)}$ order of a power of a group element.
2731
Groups of even order have an element whose order is 2.
156319
Show that a group with $|G| = 33$ contains an element of order $3$
38083
Order of conjugate of an element given the order of its conjugate
35660
Elements of order 2 in $D_{2n}$
127603
If $G$ be a group of order $8$ and $x$ be a element of order $4$. Prove that $x^2 \in Z(G)$
146221
Find the product $\prod_{n=1}^{\infty} (1+x^{2n-1}) $
83036
f(g(x)) has a degree divisible by n
15341
Non-abelian finite group in which more than half of the elements have order $2$
14815
How prove this $\prod_{1\le i<j\le n}\frac{a_{j}-a_{i}}{j-i}$ is integer
33216
Prove that the order of an element in $S_n$ equals the least common multiple of the lengths of the cycles in its cycle decomposition.
100061
The Maximum possible order for an element $S_n$
96329
Show that for any $k$-cycle $(a_1 a_2...a_k) \in S_n$, and for any permutation $\pi \in S_n$, $\pi(a_1...a_k)\pi^{-1}=(\pi(a_1)..\pi(a_k))$
71608
A property of finite field of order $2^n$
128108
$Y=\prod_{n\in\mathbb{N}}X$.
62977
Show on $\mathbb{N}$ there are $2^{\aleph_0}$ nonisomorphic linear orders.