A generalization of the Chermak--Delgado measure on subgroups and its associated lattice

Cocke, William; Kappe, Luise-Charlotte; Magidin, Arturo

doi:10.22108/ijgt.2023.138469.1859

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	A generalization of the Chermak--Delgado measure on subgroups and its associated lattice
International Journal of Group Theory
دوره 14، شماره 2، شهریور 2025، صفحه 75-91 اصل مقاله (460.68 K)
نوع مقاله: Ischia Group Theory 2022
شناسه دیجیتال (DOI): 10.22108/ijgt.2023.138469.1859
نویسندگان
William Cocke¹؛ Luise-Charlotte Kappe²؛ Arturo Magidin^* ³
¹School of Computer and Cyber Sciences, Augusta University, 100 Grace Hopper Ln, Augusta, GA 30901, USA
²Department of Mathematics and Statistics, Binghamton University, P.O. Box 6000, Binghamton, NY 13902-6000, USA
³Department of Mathematics, University of Louisiana at Lafayette, P.O. Box 43568, Lafayette LA 70504-3568 USA
چکیده
We generalize the Chermak--Delgado measure of a subgroup of a finite group $G$, $\mu(H) = \|H\|\|C_{G}(H)\|$, and its associated lattice of subgroups with maximal measure. We consider mappings $M$ of the lattice of all subgroups $\mathrm{Sub}(G)$ into itself and define a measure associated to $M$ by setting $\mu(H)=\|H\|\|M(H)\|$. We investigate under what conditions on $M$ the subgroups with maximal measure form a sublattice of $\mathrm{Sub}(G)$. In particular, our focus is on the case where $M(H)$ is a centralizer-like subgroup.
کلیدواژه‌ها
Subgroup lattice؛ characteristic subgroup؛ Chermak-Delgado lattice؛ CD-admissible function

مراجع
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A generalization of the Chermak--Delgado measure on subgroups and its associated lattice