| The influence of second maximal subgroups on the structure of group class $\mathfrak{J}_{pr}$ |
| Received:October 23, 2024 Revised:February 28, 2025 |
| Key Words:
maximal subgroups, second maximal subgroups, the class of the group $\mathfrak{J}_{pr}$
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| Fund Project:NSFC(Grant \#12371018, Grant \# 12201236), The Fundamental Research Funds for the Central Universities (Grant \# B240201093/2013) and Project supported by the Natural Science Foundation of the Anhui Higher Education Institutions of China(Grant \# 2022AH051907) |
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| Abstract: |
| In this paper, we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups. A correlation characterization of the group class $\mathfrak{J}_{pr}$ is presented by establishing the relationship between the core and the second maximal subgroups in these classifications. |
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