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arXiv · 1802.03554

Breaking points in centralizer lattices

Marius Tărnăuceanu
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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.

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Marius Tărnăuceanu. 2018-02-10. Breaking points in centralizer lattices. https://arxiv.org/abs/1802.03554

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