Year: 2025
Type: preprint
Abstract: Let $G$ be a finite group. In 2024, Cameron introduced two different concepts of independence (namely independence and strong independence) for the subsets of $G$, yielding to the definition of two simplicial complexes whose vertices are the elements of $G$. The strong independence complex $\tildeΣ(G)$ turns out to be a subcomplex of the independence complex $Σ(G)$. We discuss several invariant properties related to these complexes and ask a number of questions inspired by our results and the examples we construct. We study then the particular case of complexes on finite abelian groups, giving a characterization of the finite groups realizing them. In conclusion, answering a question of Cameron, we classify all finite groups in which the two concepts of independence coincide.
Source: arXiv (Cornell University)
Authors: Lucchini, Andrea, Stanojkovski, Mima
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G5245466801, G7933988292, G972786147
OpenAlex ID: W6979277465
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