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Restrictions on commutativity ratios in finite groups | ||
| International Journal of Group Theory | ||
| مقاله 1، دوره 3، شماره 4، اسفند 2014، صفحه 1-12 اصل مقاله (321.08 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2014.4570 | ||
| نویسندگان | ||
| Robert Heffernan* 1؛ Des MacHale2؛ Aine Ni She3 | ||
| 1University of Connecticut | ||
| 2University College Cork | ||
| 3Cork Institute of Technology | ||
| چکیده | ||
| 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 `large'. We show that if $\Pr(G) > \frac{7}{24}$, then $G$ is metabelian and we give threshold results in the cases where $G$ is insoluble and $G'$ is nilpotent. We also show that if $f(G) > \frac{1}{2}$, then $f(G) = \frac{n+1}{2n}$, for some natural number $n$. | ||
| کلیدواژهها | ||
| commutativity ratios؛ commuting probability؛ Finite groups | ||
| مراجع | ||
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