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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2602.12912 |
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| _version_ | 1866911449484361728 |
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| author | Margolis, Stuart Rhodes, John |
| author_facet | Margolis, Stuart Rhodes, John |
| contents | A base of a permutation group (X,G) is a subset B of X such that its pointwise stabilizer is the trivial group. A list (x1,x2, ... ,xk) of elements of X is irredundant if each element is not in the pointwise stabilizer of its predecessors. We define a Boolean representable simplicial complex B(X,G) such that a subset Y of X is independent if and only if some enumeration of its elements is irredundant. In addition Y is a base if and only if its closure is X. We give a number of examples and close with a conjecture whose solution leads to a new proof of the Feit-Thompson Theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_12912 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Bases of Permutation Groups and Boolean Representable Simplicial Complexes Margolis, Stuart Rhodes, John Group Theory Combinatorics 20B05, 20D05, 20E32 A base of a permutation group (X,G) is a subset B of X such that its pointwise stabilizer is the trivial group. A list (x1,x2, ... ,xk) of elements of X is irredundant if each element is not in the pointwise stabilizer of its predecessors. We define a Boolean representable simplicial complex B(X,G) such that a subset Y of X is independent if and only if some enumeration of its elements is irredundant. In addition Y is a base if and only if its closure is X. We give a number of examples and close with a conjecture whose solution leads to a new proof of the Feit-Thompson Theorem. |
| title | Bases of Permutation Groups and Boolean Representable Simplicial Complexes |
| topic | Group Theory Combinatorics 20B05, 20D05, 20E32 |
| url | https://arxiv.org/abs/2602.12912 |