Probability that an element of a finite group has a square root
Probability that an element of a finite group has a square root
Let $G$ be a finite group of even order. We give some bounds for the probability ${\rm p}(G)$ that a randomly chosen element in $G$ has a square root. In particular, we prove that ${\rm p}(G) \leq 1-{\lfloor \sqrt{|G|}\rfloor/|G|}$. Moreover, we show that