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A few remarks on the theory of non-nilpotent graphs
- Source :
- (2023), Communications in Algebra, 51:11, 4604-4613
- Publication Year :
- 2022
-
Abstract
- We prove a few results about non-nilpotent graphs of symmetric groups $S_n$ -- namely that they have a Hamiltonian cycle and they satisfy a conjecture of Nongsiang and Saikia. The latter is likewise proven for alternating groups $A_n$. We also show that the class of non-nilpotent graphs does not have any ''local'' properties, ie. for every simple graph $X$ there is a group $G$, such that its non-nilpotent graph has $X$ as an induced subgraph.
- Subjects :
- Mathematics - Group Theory
Subjects
Details
- Database :
- arXiv
- Journal :
- (2023), Communications in Algebra, 51:11, 4604-4613
- Publication Type :
- Report
- Accession number :
- edsarx.2210.00344
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1080/00927872.2023.2213771