Group theory
Breaking points in centralizer lattices
Comptes Rendus. Mathématique, Volume 356 (2018) no. 8, pp. 843-845.

In this note, we prove that the centralizer lattice C(G) of a group G cannot be written as a union of two proper intervals. In particular, it follows that C(G) has no breaking point. As an application, we show that the generalized quaternion 2-groups are not capable.

Dans cette note, nous montrons que le treillis des centralisateurs C(G) d'un groupe G ne peut pas être écrit comme une union de deux intervalles appropriés. En particulier, il s'ensuit que C(G) n'a pas de point de rupture. Comme application, nous montrons que les 2-groupes de quaternions généralisés ne sont pas capables.

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DOI: 10.1016/j.crma.2018.06.006
Tărnăuceanu, Marius 1

1 Faculty of Mathematics, “Al.I. Cuza” University, Iaşi, Romania
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Tărnăuceanu, Marius. Breaking points in centralizer lattices. Comptes Rendus. Mathématique, Volume 356 (2018) no. 8, pp. 843-845. doi : 10.1016/j.crma.2018.06.006. http://www.numdam.org/articles/10.1016/j.crma.2018.06.006/

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