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$4$-Regular prime graphs of nonsolvable groups | ||
| International Journal of Group Theory | ||
| مقاله 18، دوره 9، شماره 3، آذر 2020، صفحه 193-222 اصل مقاله (324.79 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2019.112277.1490 | ||
| نویسندگان | ||
| Donnie Kasyoki1؛ Paul Oleche* 2 | ||
| 1School of Mathematics, Statistics and Actuarial Science, Maseno University, Kenya | ||
| 2Department of Pure and Mathematics, Maseno University, P.O. Box 333, Maseno, Kenya | ||
| چکیده | ||
| Let $G$ be a finite group and cd$(G)$ denote the character degree set for $G$. The prime graph $Δ(G)$ is a simple graph whose vertex set consists of prime divisors of elements in cd$(G)$, denoted $\rho(G)$. Two primes $p,q\in \rho(G)$ are adjacent in $Δ(G)$ if and only if $pq|a$ for some $a\in cd(G)$. We determine which simple $4$-regular graphs occur as prime graphs for some finite nonsolvable group. | ||
| کلیدواژه‌ها | ||
| Nonsolvable group؛ character؛ character degree؛ graph؛ prime graph | ||
| مراجع | ||
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