On solvability of the first Hochschild cohomology of odd p-groups

Matthew Antrobus

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arXiv · 2512.14555

On solvability of the first Hochschild cohomology of odd p-groups

Matthew Antrobus

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Abstract

We give a necessary and sufficient criterion for the solvability of $\operatorname{HH}^1(kP)$ as a Lie algebra, where $P$ is a $p$-group with $p$ odd, in terms of a directed graph constructed from the group $P$. This gives non-trivial results on the structure of such Lie algebras.

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Matthew Antrobus. 2025-12-16. On solvability of the first Hochschild cohomology of odd p-groups. https://arxiv.org/abs/2512.14555

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