Abstract
Let H be a subgroup of a finite group G. We say that H satisfies the partial \( \Pi \)-property in G if there exists a chief series \( \varGamma _{G}: 1 =G_{0}< G_{1}< \cdots < G_{n}= G \) of G such that for every G-chief factor \( G_{i}/G_{i-1} (1\le i\le n) \) of \( \varGamma _{G} ,\) \( | G / G_{i-1}: N _{G/G_{i-1}} (HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1})| \) is a \( \pi (HG_{i-1}/G_{i-1}\cap G_{i}/G_{i-1}) \)-number. In this paper, we study the influence of some subgroups of prime power order satisfying the partial \( \Pi \)-property on the structure of a finite group.
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Acknowledgements
This work is supported by the National Natural Science Foundation of China (Grant No. 12071376, 11971391) and the Fundamental Research Funds for the Central Universities (No. XDJK2020B052).
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Qiu, Z., Liu, J. & Chen, G. On the Partial \( \Pi \)-Property of Some Subgroups of Prime Power Order of Finite Groups. Mediterr. J. Math. 21, 61 (2024). https://doi.org/10.1007/s00009-024-02603-6
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DOI: https://doi.org/10.1007/s00009-024-02603-6