Abstract
Given a finite group G, we denote by L(G) the subgroup lattice of G and by \({\mathcal{C}\mathcal{D}}(G)\) the Chermak–Delgado lattice of G. In this note, we study finite groups G such that the set \(L_G\) of subgroups of G with minimum Chermak–Delgado measure forms a sublattice of L(G).
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Data availability
Data openly available in a public repository, with a permanent identifier.
References
An, L., Brennan, J.P., Qu, H., Wilcox, E.: Chermak–Delgado lattice extension theorems. Commun. Algebra 43, 2201–2213 (2015)
Brewster, B., Wilcox, E.: Some groups with computable Chermak–Delgado lattices. Bull. Aus. Math. Soc. 86, 29–40 (2012)
Brewster, B., Hauck, P., Wilcox, E.: Groups whose Chermak–Delgado lattice is a chain. J. Group Theory 17, 253–279 (2014)
Chermak, A., Delgado, A.: A measuring argument for finite groups. Proc. AMS 107, 907–914 (1989)
Isaacs, I.M.: Finite Group Theory. American Mathematical Society, Providence, RI (2008)
McCulloch, R.: Chermak–Delgado simple groups. Commun. Algebra 45, 983–991 (2017)
McCulloch, R., Tărnăuceanu, M.: Two classes of finite groups whose Chermak–Delgado lattice is a chain of length zero. Commun. Algebra 46, 3092–3096 (2018)
McCulloch, R., Tărnăuceanu, M.: On the Chermak–Delgado lattice of a finite group. Commun. Algebra 48, 37–44 (2020)
Schmidt, R.: Subgroup Lattices of Groups, de Gruyter Expositions in Mathematics 14. de Gruyter, Berlin (1994)
Suzuki, M.: Group Theory, I, II, Springer, Berlin, 1982 (1986)
Tărnăuceanu, M.: A note on the Chermak–Delgado lattice of a finite group. Commun. Algebra 46, 201–204 (2018)
Tărnăuceanu, M.: Finite groups with a certain number of values of the Chermak–Delgado measure. J. Algebra Appl. 19, 2050088 (2020)
Wilcox, E.: Exploring the Chermak–Delgado lattice. Math. Mag. 89, 38–44 (2016)
Morresi Zuccari, A., Russo, V., Scoppola, C.M.: The Chermak–Delgado measure in finite \(p\)-groups. J. Algebra 502, 262–276 (2018)
Acknowledgements
The author is grateful to the reviewer for its remarks which improve the previous version of the paper.
Funding
The author did not receive support from any organization for submitted work.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The author declares that she has no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Fasolă, G. On the Chermak–Delgado Measure of a Finite Group. Results Math 79, 44 (2024). https://doi.org/10.1007/s00025-023-02080-5
Received:
Accepted:
Published:
DOI: https://doi.org/10.1007/s00025-023-02080-5