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

• Autorzy: M. S. Lucido , M. R. Pournaki
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 20P05: Probabilistic methods in group theory
• 20D60: Arithmetic and combinatorial problems
• 20A05: Axiomatics and elementary properties
• 05A15: Exact enumeration problems, generating functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2008
• Tom: 112
• Numer: 1
• Strony: 147-155

Daty

wydano

2008

Twórcy

autor

M. S. Lucido

• Dipartimento di Matematica e Informatica, Università di Udine, Via delle Scienze 208, I-33100 Udine, Italy

autor

M. R. Pournaki

• Department of Mathematical Sciences, Sharif University of Technology, P.O. Box 11155-9415, Tehran, Iran
• School of Mathematics, Institute for Studies in Theoretical Physics and Mathematics, P.O. Box 19395-5746, Tehran, Iran

Identyfikatory

DOI

10.4064/cm112-1-7