Author/Authors :
هفرنان ، رابرت نويسنده Department of Mathematics, University of Connecticut, Storrs, USA Heffernan, Robert , ماچال، دس نويسنده Department of Mathematics, University College Cork Cork, Ireland MacHale, Des , ني شي، آنيه نويسنده Department of Mathematics, Cork Institute of Technology Cork, Ireland Ni She, Aine
Abstract :
We consider two commutativity ratios Pr(G) and f(G) in a finite group G and examine
the properties of G when these ratios are `largeʹ. We show that if Pr(G) > 7
24 , then G is metabelian
and we give threshold results in the cases where G is insoluble and G0 is nilpotent. We also show that
if f(G) > 1
2 , then f(G) = n+1
2n , for some natural number n.
