Abstract
A subgroup H of a finite group G is called a c#-normal subgroup of G if there exists a normal subgroup K of G such that G = HK and H ∩ K is a CAP-subgroup of G: In this paper, we investigate the influence of fewer c#-normal subgroups of Sylow p-subgroups on the p-supersolvability, p-nilpotency, and supersolvability of finite groups. We obtain some new sufficient and necessary conditions for a group to be p-supersolvable, p-nilpotent, and supersolvable. Our results improve and extend many known results.
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Acknowledgements
The authors would like to thank the referees for their helpful suggestions. This work was supported by the National Natural Science Foundation of China (Grant No. 11361006) and SRF of Guangxi University (No. XGZ130761).
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Wei, H., Dai, Q., Zhang, H. et al. On c#-normal subgroups infinite groups. Front. Math. China 13, 1169–1178 (2018). https://doi.org/10.1007/s11464-018-0724-x
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DOI: https://doi.org/10.1007/s11464-018-0724-x