The simple $\mathscr{B}_ψ$-groups
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911035491876864 |
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| author | Azad, Morteza Baniasad |
| author_facet | Azad, Morteza Baniasad |
| contents | In a finite group $ G $, $ ψ(G) $ denotes the sum of element orders of $ G $.
A finite group $ G $ is said to be a $\mathscr{B}_ψ$-group if $ ψ(H) < |G| $ for any proper subgroup $ H $ of $ G $.
In \cite{Lazorec} Lazorec asked: "what can be said about the $\mathscr{B}_ψ$ property of the finite simple groups $ \operatorname{PSL}(2, q) $?" In this paper, we answer this question for the case of not only the finite simple groups $ \operatorname{PSL}(2, q) $ but also all other finite simple groups. We show that if $ S $ is a finite simple group, such that $ S \neq Alt(n) $ for any $ n \geq 14 $, then $S$ is a $\mathscr{B}_ψ$-group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_03881 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The simple $\mathscr{B}_ψ$-groups Azad, Morteza Baniasad Group Theory 20D05, 20D60, 20D06, 20D08 In a finite group $ G $, $ ψ(G) $ denotes the sum of element orders of $ G $. A finite group $ G $ is said to be a $\mathscr{B}_ψ$-group if $ ψ(H) < |G| $ for any proper subgroup $ H $ of $ G $. In \cite{Lazorec} Lazorec asked: "what can be said about the $\mathscr{B}_ψ$ property of the finite simple groups $ \operatorname{PSL}(2, q) $?" In this paper, we answer this question for the case of not only the finite simple groups $ \operatorname{PSL}(2, q) $ but also all other finite simple groups. We show that if $ S $ is a finite simple group, such that $ S \neq Alt(n) $ for any $ n \geq 14 $, then $S$ is a $\mathscr{B}_ψ$-group. |
| title | The simple $\mathscr{B}_ψ$-groups |
| topic | Group Theory 20D05, 20D60, 20D06, 20D08 |
| url | https://arxiv.org/abs/2309.03881 |