Probability that an element of a finite group has a square root

M. S. Lucido, and M. R. Pournaki. "Probability that an element of a finite group has a square root." Colloquium Mathematicae 112.1 (2008): 147-155. <http://eudml.org/doc/286372>.

@article{M2008,
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 2-subgroup 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.},
author = {M. S. Lucido, M. R. Pournaki},
journal = {Colloquium Mathematicae},
keywords = {finite groups; probability; random elements},
language = {eng},
number = {1},
pages = {147-155},
title = {Probability that an element of a finite group has a square root},
url = {http://eudml.org/doc/286372},
volume = {112},
year = {2008},
}

TY - JOUR
AU - M. S. Lucido
AU - M. R. Pournaki
TI - Probability that an element of a finite group has a square root
JO - Colloquium Mathematicae
PY - 2008
VL - 112
IS - 1
SP - 147
EP - 155
AB - 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 2-subgroup 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.
LA - eng
KW - finite groups; probability; random elements
UR - http://eudml.org/doc/286372
ER -