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

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.5802/crmath.18
Classification : 20C15
Keywords: 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.
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
@article{CRMATH_2020__358_1_109_0,
     author = {Burkett, Shawn T. and Lewis, Mark L.},
     title = {A characterization of {Nested} {Groups} in terms of conjugacy classes},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {109--112},
     year = {2020},
     publisher = {Acad\'emie des sciences, Paris},
     volume = {358},
     number = {1},
     doi = {10.5802/crmath.18},
     language = {en},
     url = {https://www.numdam.org/articles/10.5802/crmath.18/}
}
TY  - JOUR
AU  - Burkett, Shawn T.
AU  - Lewis, Mark L.
TI  - A characterization of Nested Groups in terms of conjugacy classes
JO  - Comptes Rendus. Mathématique
PY  - 2020
SP  - 109
EP  - 112
VL  - 358
IS  - 1
PB  - Académie des sciences, Paris
UR  - https://www.numdam.org/articles/10.5802/crmath.18/
DO  - 10.5802/crmath.18
LA  - en
ID  - CRMATH_2020__358_1_109_0
ER  - 
%0 Journal Article
%A Burkett, Shawn T.
%A Lewis, Mark L.
%T A characterization of Nested Groups in terms of conjugacy classes
%J Comptes Rendus. Mathématique
%D 2020
%P 109-112
%V 358
%N 1
%I Académie des sciences, Paris
%U https://www.numdam.org/articles/10.5802/crmath.18/
%R 10.5802/crmath.18
%G en
%F CRMATH_2020__358_1_109_0
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

[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

Cité par Sources :