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FINITE GROUPS WITH LARGE CHERMAK–DELGADO LATTICES

Part of: Representation theory of groups

Published online by Cambridge University Press:  25 August 2022

GEORGIANA FASOLĂ Open the ORCID record for GEORGIANA FASOLĂ [Opens in a new window]  and
MARIUS TǍRNǍUCEANU Open the ORCID record for MARIUS TǍRNǍUCEANU [Opens in a new window]
GEORGIANA FASOLĂ
Affiliation:
Faculty of Mathematics, ‘Al.I. Cuza’ University, Iaşi, Romania e-mail: georgiana.fasola@student.uaic.ro
MARIUS TǍRNǍUCEANU*
Affiliation:
Faculty of Mathematics, ‘Al.I. Cuza’ University, Iaşi, Romania
*
e-mail: tarnauc@uaic.ro
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Abstract

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 $k=1,2$.

Keywords

Chermak–Delgado measureChermak–Delgado latticesubgroup latticegeneralised quaternion 2-group

MSC classification

Primary: 20D30: Series and lattices of subgroups
Secondary: 20D60: Arithmetic and combinatorial problems 20D99: None of the above, but in this section

Information

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 107 , Issue 3 , June 2023 , pp. 451 - 455
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Copyright
© The Author(s), 2022. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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