product of elements $\ne e$ implies only one element with order $2$
121077
Product of all elements in finite group
15633
If G is a group of even order, prove it has an element $a \neq e$ satisfying $a^2 = e$.
102971
Product of all elements of a finite group with an unique element of order 2
85882
Show that $1\otimes (1,1,\ldots)\neq 0$ in $\mathbb{Q} \otimes_{\mathbb{Z}} \prod_{n=2}^{\infty} (\mathbb{Z}/n \mathbb{Z})$.
138862
Product of all elements in an odd finite abelian group is 1
119758
On the order of elements of $\mathrm{GL}(2,q)$.
16971
Prove that no ordinal is an element of itself
110464
Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
28266
For $n\geq 3$ there exist $x,y\in S_n$ such that $x$ and $y$ have order $2$ and $xy$ has order $n$.
109034
Does a finite $[E:K]_s$ imply that $[E_s:K]$ is finite?
113411
If $E$ is generated by $E_1$ and $E_2$, then $[E:F]\leq [E_1:F][E_2:F]$?
45523
Can the product of two non invertible elements in a ring be invertible?
76347
Shorter proof for some equvalences
98734
Order of a product of elements in a generic group
100061
The Maximum possible order for an element $S_n$
1577
Order of nontrivial elements is 2 implies Abelian group
152820
Every element of a group has order $2$. Why, intuitively, is it abelian?