On the 𝑝’-extensions of inertial blocks

Zhou, Yuanyang

doi:10.1090/proc/12691

On the $p’$-extensions of inertial blocks
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Proc. Amer. Math. Soc. 144 (2016), 41-54 Request permission

Abstract:

Let $p$ be a prime number, $G$ a finite group, $H$ a normal subgroup of $G$, and $b$ a $p$-block of $H$. Assuming that the index of $H$ in $G$ is coprime to $p$, we prove that any $p$-block of $G$ covering $b$ is inertial if and only if the block $b$ is inertial.

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