FINITE GROUPS WITH LARGE CHERMAK–DELGADO LATTICES

FINITE GROUPS WITH LARGE CHERMAK–DELGADO LATTICES

Given a finite group G, we denote by $L(G)$ the subgroup lattice of G and by ${\cal CD}(G)$ the Chermak–Delgado lattice of G. In this note, we determine the finite groups G such that $|{\cal CD}(G)|=|L(G)|-k$ , for $k=1,2$ .

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Veröffentlicht in:Bulletin of the Australian Mathematical Society 2023-06, Vol.107 (3), p.451-455
Hauptverfasser: FASOLĂ, GEORGIANA, TǍRNǍUCEANU, MARIUS
Format: Artikel
Sprache:eng
Schlagworte:
Group theory
Hypotheses
Lattices (mathematics)
Subgroups
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Zusammenfassung:Given a finite group G, we denote by $L(G)$ the subgroup lattice of G and by ${\cal CD}(G)$ the Chermak–Delgado lattice of G. In this note, we determine the finite groups G such that $|{\cal CD}(G)|=|L(G)|-k$ , for $k=1,2$ .
ISSN:0004-9727
1755-1633
DOI:10.1017/S0004972722000806