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On the $ p'$-extensions of inertial blocks


Author: Yuanyang Zhou
Journal: Proc. Amer. Math. Soc. 144 (2016), 41-54
MSC (2010): Primary 20C20
Published electronically: September 24, 2015
MathSciNet review: 3415575
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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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Additional Information

Yuanyang Zhou
Affiliation: Department of Mathematics and Statistics, Central China Normal University, Wuhan, 430079, People’s Republic of China
Email: zhouyuanyang@mail.ccnu.edu.cn

DOI: https://doi.org/10.1090/proc/12691
Received by editor(s): January 9, 2014
Received by editor(s) in revised form: December 5, 2014
Published electronically: September 24, 2015
Additional Notes: The author was supported by self-determined research funds of CCNU from the colleges’ basic research and operation of MOE (No. 20205140052) and by NSFC (No. 11071091)
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2015 American Mathematical Society