On the base size of a finite group on its action on the lattice of subgroups
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866910190968766464 |
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| author | Du, JiaLi Morris, Joy Spiga, Pablo |
| author_facet | Du, JiaLi Morris, Joy Spiga, Pablo |
| contents | Given a finite group $R$, we investigate the base size of the action of the automorphism group of $R$ on the lattice of subgroups of $R$. Our main result shows that this base size is $1$ if and only if $R$ is cyclic. Our motivation arises from a conjecture of Babai on the problem of representing groups as automorphism groups of lattices with a bounded number of orbits. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_03449 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On the base size of a finite group on its action on the lattice of subgroups Du, JiaLi Morris, Joy Spiga, Pablo Group Theory Combinatorics Given a finite group $R$, we investigate the base size of the action of the automorphism group of $R$ on the lattice of subgroups of $R$. Our main result shows that this base size is $1$ if and only if $R$ is cyclic. Our motivation arises from a conjecture of Babai on the problem of representing groups as automorphism groups of lattices with a bounded number of orbits. |
| title | On the base size of a finite group on its action on the lattice of subgroups |
| topic | Group Theory Combinatorics |
| url | https://arxiv.org/abs/2605.03449 |