no. 1
Théorie des groupes
A characterization of Nested Groups in terms of conjugacy classes
[Une caractérisation des groupes emboîtés en termes de classes de conjugaison]
Burkett, Shawn T.1 ; Lewis, Mark L.1 
1 Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, U.S.A.
Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 109-112.

Un groupe est emboîté si les centres des caractères irréductibles forment une chaîne. Dans cet article, nous montrerons qu’il existe un ensemble de sous-groupes associés aux classes de conjugaison de groupe tel qu’un groupe est emboîté si et seulement si ces sous-groupes forment une chaîne.

A group is nested if the centers of the irreducible characters form a chain. In this paper, we will show that there is a set of subgroups associated with the conjugacy classes of group so that a group is nested if and only if these subgroups form a chain.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.18
Classification : 20C15
Mots clés : nested groups, nested GVZ groups, conjugacy classes
Burkett, Shawn T. 1 ; Lewis, Mark L. 1

1 Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242, U.S.A. 
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     title = {A characterization of {Nested} {Groups} in terms of conjugacy classes},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {109--112},
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     year = {2020},
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Burkett, Shawn T.; Lewis, Mark L. A characterization of Nested Groups in terms of conjugacy classes. Comptes Rendus. Mathématique, Tome 358 (2020) no. 1, pp. 109-112. doi : 10.5802/crmath.18. http://www.numdam.org/articles/10.5802/crmath.18/

[1] Berkovich, Yakov Groups of prime power order. Vol. 1, de Gruyter Expositions in Mathematics, 46, Walter de Gruyter, 2008 | MR | Zbl

[2] Burkett, Shawn T.; Lewis, Mark L. GVZ-groups (2019) (https://arxiv.org/abs/1909.05841, submitted)

[3] Burkett, Shawn T.; Lewis, Mark L. Groups where the centers of the irreducible characters form a chain II, Monatsh. Math. (2020) | DOI

[4] Chillag, David On Blichfeldt’s like congruences and other close characters—conjugacy classes analogs, Ischia group theory 2008, World Scientific, 2008, pp. 42-55 | Zbl

[5] Lewis, Mark L. Groups where the centers of the irreducible characters form a chain, Monatsh. Math. (2020) | DOI

[6] Nenciu, Adriana Isomorphic character tables of nested GVZ-groups, J. Algebra Appl., Volume 11 (2012) no. 2, 1250033, 12 pages | MR | Zbl

[7] Nenciu, Adriana Nested GVZ-groups, J. Group Theory, Volume 19 (2016) no. 4, pp. 693-704 | MR | Zbl

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