The non-two-primes graph of a finite group

Garatea-Zaballa, Karmele; Lucchini, Andrea

doi:10.22108/toc.2025.142373.2201

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	The non-two-primes graph of a finite group
Transactions on Combinatorics
مقالات آماده انتشار، اصلاح شده برای چاپ، انتشار آنلاین از تاریخ 14 دی 1403 اصل مقاله (444.87 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.142373.2201
نویسندگان
Karmele Garatea-Zaballa؛ Andrea Lucchini^*
Dipartimento di Matematica “Tullio Levi Civita”, Università di Padova, Via Trieste 63, 35121 Padova, Italy
چکیده
To any finite group $G$, we may associate a graph whose vertices are the elements of $G$ and where two distinct vertices $x$ and $y$ are adjacent if and only if the order of the subgroup $\langle x, y\rangle$ is divisible by at least 3 distinct primes. We prove that the subgraph of this graph induced by the non-isolated vertices is connected and has diameter at most 5.
کلیدواژه‌ها
finite groups؛ order of elements؛ graphs associated to finite groups

مراجع
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The non-two-primes graph of a finite group