Abstract
Let G be a finite group. A subgroup H of G is called an NE-subgroup of G if it satisfies H G∩N G (H)=H. A subgroup H of G is said to be a N E ∗-subgroup of G if there exists a subnormal subgroup T of G such that G=H T and H∩T is a NE-subgroup of G. In this article, we investigate the structure of G under the assumption that subgroups of prime order are N E ∗-subgroups of G. The finite groups, all of whose minimal subgroups of the generalized Fitting subgroup are N E ∗-subgroups are classified.
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Acknowledgements
The authors are very grateful to the referee for his/her careful reading of the paper and for accurate suggestions which helped in improving the earlier version of this paper. This work was partially supported by the National Natural Science Foundation of China (11261007, 11326055, 11461007), the Science Foundation of Guangxi (2014GXNSFAA118009, 2013GXNSFBA019003), and the Foundation of Guangxi Education Department (ZD2014016).
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LI, Y., ZHONG, X. Finite groups all of whose minimal subgroups are N E ∗-subgroups. Proc Math Sci 124, 501–509 (2014). https://doi.org/10.1007/s12044-014-0202-7
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DOI: https://doi.org/10.1007/s12044-014-0202-7