Dans cette note, nous montrons que le treillis des centralisateurs d'un groupe G ne peut pas être écrit comme une union de deux intervalles appropriés. En particulier, il s'ensuit que n'a pas de point de rupture. Comme application, nous montrons que les 2-groupes de quaternions généralisés ne sont pas capables.
In this note, we prove that the centralizer lattice of a group G cannot be written as a union of two proper intervals. In particular, it follows that has no breaking point. As an application, we show that the generalized quaternion 2-groups are not capable.
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@article{CRMATH_2018__356_8_843_0, author = {T\u{a}rn\u{a}uceanu, Marius}, title = {Breaking points in centralizer lattices}, journal = {Comptes Rendus. Math\'ematique}, pages = {843--845}, publisher = {Elsevier}, volume = {356}, number = {8}, year = {2018}, doi = {10.1016/j.crma.2018.06.006}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2018.06.006/} }
TY - JOUR AU - Tărnăuceanu, Marius TI - Breaking points in centralizer lattices JO - Comptes Rendus. Mathématique PY - 2018 SP - 843 EP - 845 VL - 356 IS - 8 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2018.06.006/ DO - 10.1016/j.crma.2018.06.006 LA - en ID - CRMATH_2018__356_8_843_0 ER -
Tărnăuceanu, Marius. Breaking points in centralizer lattices. Comptes Rendus. Mathématique, Tome 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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