Non-commuting graph of AC-groups: as matroids
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908369150803968 |
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| author | Azad, Azizollah Karimi, Nasim Rahbariyan, Sakineh |
| author_facet | Azad, Azizollah Karimi, Nasim Rahbariyan, Sakineh |
| contents | Let G be a non-abelian group and let Z(G) be the center of G. Associate a graph ΓG (called non-commuting graph of G) as follows: Take G\Z(G) as the vertices of ΓG and join x and y, whenever $xy \not= yx$. In this paper, we show that a finite group G is an AC-group, if and only if, the associated non-commuting graph of G is a matroid. Leveraging the properties of matroids, we further delve into the characteristics of AC-groups. Additionally, we provide a formula to compute the clique number of the non-commuting graph of AC-groups, offering a new perspective on the structure of these groups |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12070 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Non-commuting graph of AC-groups: as matroids Azad, Azizollah Karimi, Nasim Rahbariyan, Sakineh Group Theory Let G be a non-abelian group and let Z(G) be the center of G. Associate a graph ΓG (called non-commuting graph of G) as follows: Take G\Z(G) as the vertices of ΓG and join x and y, whenever $xy \not= yx$. In this paper, we show that a finite group G is an AC-group, if and only if, the associated non-commuting graph of G is a matroid. Leveraging the properties of matroids, we further delve into the characteristics of AC-groups. Additionally, we provide a formula to compute the clique number of the non-commuting graph of AC-groups, offering a new perspective on the structure of these groups |
| title | Non-commuting graph of AC-groups: as matroids |
| topic | Group Theory |
| url | https://arxiv.org/abs/2505.12070 |