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In this note, we prove that the centralizer lattice ${\mathfrak C}(G)$ of a group $G$ cannot be written as a union of two proper intervals. In particular, it follows that… Click to show full abstract
In this note, we prove that the centralizer lattice ${\mathfrak C}(G)$ of a group $G$ cannot be written as a union of two proper intervals. In particular, it follows that ${\mathfrak C}(G)$ has no breaking point. As an application, we show that the generalized quaternion $2$-groups are not capable.
Keywords:
centralizer lattices;
centralizer;
points centralizer;
breaking points
Journal Title: Comptes Rendus Mathematique
Year Published: 2018
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Journal Title: Comptes Rendus Mathematique
Year Published: 2018
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!