Abstract Let be a finite group. In 10, two different concepts of independence (namely, independence and strong independence ) are introduced for the subsets of , yielding to the definition of two simplicial complexes whose vertices are the elements of . The strong independence complex turns out to be a subcomplex of the independence complex . 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 Peter Cameron, we classify all finite groups in which the two concepts of independence coincide.
Lucchini et al. (Mon,) studied this question.
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