Non-cyclic graph associated with a group
| dc.creator | Abdollahi, Alireza | |
| dc.creator | Hassanabadi, A. Mohammadi | |
| dc.date | 2008-10-02 | |
| dc.date.accessioned | 2026-07-07T10:07:02Z | |
| dc.date.available | 2026-07-07T10:07:02Z | |
| dc.description | We associate a graph $\mathcal{C}_G$ to a non locally cyclic group $G$ (called the non-cyclic graph of $G$) as follows: take $G\backslash Cyc(G)$ as vertex set, where $Cyc(G)=\{x\in G | < x,y> \text{is cyclic for all} y\in G\}$ is called the cyclicizer of $G$, and join two vertices if they do not generate a cyclic subgroup. For a simple graph $Γ$, $w(Γ)$ denotes the clique number of $Γ$, which is the maximum size (if it exists) of a complete subgraph of $Γ$. In this paper we characterize groups whose non-cyclic graphs have clique numbers at most 4. We prove that a non-cyclic group $G$ is solvable whenever $w(\mathcal{C}_G)<31$ and the equality for a non-solvable group $G$ holds if and only if $G/Cyc(G)\cong A_5$ or $S_5$. | |
| dc.description | to appear in Journal of Algebra and its Applications | |
| dc.identifier | https://arxiv.org/abs/0810.0345 | |
| dc.identifier | http://arxiv.org/abs/0810.0345 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170494 | |
| dc.subject | Group Theory | |
| dc.subject | Combinatorics | |
| dc.subject | 20D60; 05C25 | |
| dc.title | Non-cyclic graph associated with a group | |
| dc.type | text |