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
مقاله 4، 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
[1] L. An, Groups whose Chermak–Delgado lattice is a quasi-antichain, J. Group Theory, 22 no. 3 (2019) 529–544. http://dx.doi.org/10.1515/jgth-2018-0043 [2] B. Brewster, P. Hauck and E. Wilcox, Quasi-antichain Chermak-Delgado lattices of finite groups, Arch. Math. (Basel), 103 no. 4 (2014) 301–311. [3] D. Burrell, W. Cocke and R. McCulloch, On groups with few subgroups not in the Chermak–Delgado lattice, Arnold Math. J., (2023) (to appear). [4] A. Chermak and A. Delgado, A measuring argument for finite groups, Proc. Amer. Math. Soc., 107 no. 4 (1989) 907–914. [5] W. Cocke, Subnormality and the Chermak–Delgado lattice, J. Algebra Appl., 19 no. 8 (2020) 7 pp. [6] P. Hall, Verbal and marginal subgroups, J. Reine Angew. Math., 182 (1940) 156–157. [7] I. M. Isaacs, Finite group theory, Graduate Studies in Mathematics, 92, American Mathematical Society, Providence, RI, 2008. [8] L.-C. Kappe, On n-Levi groups, Arch. Math. (Basel), 47 no. 3 (1986) 198–210. [9] L.-C. Kappe and P. M. Ratchford, On centralizer-like subgroups associated with the n-Engel word, Algebra Colloq., 6 no. 1 (1999) 1–8. [10] R. McCulloch, Finite groups with a trivial Chermak-Delgado subgroup, J. Group Theory, 21 no. 3 (2018) 449–461. [11] R. McCulloch and M. Tărnăuceanu, On the Chermak–Delgado lattice of a finite group, Comm. Algebra, 48 no. 1 (2020) 37–44. [12] M. Tărnăuceanu, Finite groups with a certain number of values of the Chermak–Delgado measure, J. Algebra Appl., 19 no. 5 (2020) 7 pp. [13] A. Morresi Zuccari, V. Russo and C. M. Scoppola, The Chermak-Delgado measure in finite p-groups, J. Algebra, 502 (2018) 262–276.
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A generalization of the Chermak--Delgado measure on subgroups and its associated lattice