Abstract
A subgroup H of a finite group G is said to be weakly \(\mathcal {H}C\)-embedded in G if there exists a normal subgroup T of G such that \(H^G = HT\) and \(H^g \cap N_T(H) \le H\) for all \(g \in G\), where \(H^G\) is the normal closure of H in G. In this paper, we investigate the structure of the finite group G under the assumption that P a Sylow p-subgroup of G, where p is a prime dividing the order of G, and we fix a subgroup of P of order d with \(1< d < \left| P\right| \) such that every subgroup H of P of order \(p^nd ~(n = 0, 1)\) is weakly \(\mathcal {H}C\)-embedded in G.
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Communicated by Mohammad Reza Darafsheh.
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Guo, Q., He, X. & Liang, J. Finite Groups with Weakly \(\mathcal {H}C\)-Embedded Subgroups. Bull. Iran. Math. Soc. 46, 1493–1500 (2020). https://doi.org/10.1007/s41980-019-00338-9
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DOI: https://doi.org/10.1007/s41980-019-00338-9