Geodesic
The A-Möbius function of a finite group
Ars Mathematica Contemporanea, Tome 23 (2023) no. 3, article no. 08, 14 p.

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The Möbius function of the subgroup lattice of a finite group G has been introduced by Hall and applied to investigate several different questions. We propose the following generalization. Let A be a subgroup of the automorphism group Aut(G) of a finite group G and denote by CA(G) the set of A-conjugacy classes of subgroups of G. For H ≤ G let [H]A = { Ha ∣ a∈ A} be the element of CA(G) containing H. We may define an ordering in CA(G) in the following way: [H]A ≤ [K]A if Ha ≤ K for some a ∈ A. We consider the Möbius function μA of the corresponding poset and analyse its properties and possible applications.
DOI : 10.26493/1855-3974.2694.56a
Keywords: Groups, subgroup lattice, Möbius function 
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Francesa Dalla Volta; Andrea Lucchini. The A-Möbius function of a finite group. Ars Mathematica Contemporanea, Tome 23 (2023) no. 3, article  no. 08, 14 p. doi : 10.26493/1855-3974.2694.56a. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.2694.56a/

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