The equation $x^2=a$ in a finite group $G$ of odd order.
121929
What finite groups always have a square root for each element?
147596
Number of solutions to $x^n=e$ in group $G$ is divisible by $n$
138862
Product of all elements in an odd finite abelian group is 1
112974
The $h-$th power of every element in a finite group of order $h$ is the identity element of the group
143550
Order of product of two elements in an abelian group
156319
Show that a group with $|G| = 33$ contains an element of order $3$
7085
Prove that if the equation $x^{2} \equiv a\pmod{pq}$ has any solutions, then it has four solutions.
8742
Examples and further results about the order of the product of two elements in a group
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
125640
Group of order $p^2$ is abelian.
22632
Galois group of $x^4-2$
9422
Computing the Galois group of polynomials $x^n-a \in \mathbb{Q}[x]$
9110
Let G be a group such that $(xy)^2 = (yx)^2$ for all x, y ∈ G. Show that $xy^2 = y^2x$ for all x, y ∈ G.
83654
Order of an element in a finite cyclic group
116080
Let G be a finite group with more than one element. Show that G has an element of prime order
109286
Galois group of $x^4-2x^2-2$
121423
Prove that every element of a finite group has an order