“School of Mathematics”
Back to Papers HomeBack to Papers of School of Mathematics
Paper IPM / M / 8585  


Abstract:  
Let G be a finite group of even order. We
give some bounds for the probability p(G) that a randomly
chosen element in G has a square root. In particular, we prove
that p(G) ≤ 1−⎣√G⎦/G. Moreover,
we show that if the Sylow 2subgroup of G is not a proper normal
elementary abelian subgroup of G, then p(G) ≤ 1−1/√G. Both of these bounds are best possible upper bounds
for p(G), depending only on the order of G.
Download TeX format 

back to top 