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Keywords:
class of group; maximal subgroup; second maximal subgroup; solvable group
class of group; maximal subgroup; second maximal subgroup; solvable group
Summary:
We aim at characterizing solvable groups with the aid of core relations between the second maximal subgroup and corresponding maximal subgroups. As applications, the related classes of generalized $p$-local groups are also studied.
References:
[1] Ballester-Bolinches, A., Ezquerro, L. M.: Classes of Finite Groups. Mathematics and its Applications (Springer) 584. Springer, Dordrecht (2006). DOI 10.1007/1-4020-4719-3 | MR 2241927 | Zbl 1102.20016
[2] Bianchi, M., Mauri, A. G. B., Hauck, P.: On finite groups with nilpotent Sylow-normalizers. Arch. Math. 47 (1986), 193-197. DOI 10.1007/BF01191993 | MR 0861865 | Zbl 0605.20017
[3] Demina, E. N., Maslova, N. V.: Nonabelian composition factors of a finite group with arithmetic constraints on nonsolvable maximal subgroups. Proc. Steklov Inst. Math. 289 (2015), S64--S76. DOI 10.1134/S0081543815050065 | MR 3364145 | Zbl 1329.20021
[4] Gao, Z., Li, J., Miao, L.: On $CAP_{S_p^*}$-subgroups of finite groups. Commun. Algebra 49 (2021), 1120-1127. DOI 10.1080/00927872.2020.1828443 | MR 4219864 | Zbl 1473.20027
[5] Gao, Z., Qiao, S., Shi, H., Miao, L.: On $p$-CAP-subgroups of finite groups. Front. Math. China 15 (2020), 915-921. DOI 10.1007/s11464-020-0866-5 | MR 4173404 | Zbl 1506.20018
[6] Guo, W.: The Theory of Classes of Groups. Mathematics and its Applications (Dordrecht) 505. Science Press, Beijing (2000). DOI 10.1007/978-94-011-4054-6 | MR 1862683 | Zbl 1005.20016
[7] Guo, X., Shum, K. P.: Cover-avoidance properties and the structure of finite groups. J. Pure Appl. Algebra 181 (2003), 297-308. DOI 10.1016/S0022-4049(02)00327-4 | MR 1975303 | Zbl 1028.20014
[8] Huppert, B.: Normalteiler und maximale Untergruppen endlicher Gruppen. Math. Z. 60 (1954), 409-434 German. DOI 10.1007/BF01187387 | MR 0064771 | Zbl 0057.25303
[9] Li, S., Liu, H., Liu, D.: The solvability between finite groups and semi-subnormal-cover- avoidance subgroups. J. Math. 37 (2017), 1303-1308 Chinese.
[10] Meng, H., Guo, X.: Weak second maximal subgroups in solvable groups. J. Algebra 517 (2019), 112-118. DOI 10.1016/j.jalgebra.2018.09.029 | MR 3869269 | Zbl 1439.20007
[11] Miao, L., Zhou, W., Gao, Z., Gao, B., Liu, W.: On second maximal subgroups with core relation in finite group. Commun. Algebra 52 (2024), 2430-2436. DOI 10.1080/00927872.2023.2301520 | MR 4728954 | Zbl 1537.20042
[12] Tate, J.: Nilpotent quotient groups. Topology 3 (1964), 109-111. DOI 10.1016/0040-9383(64)90008-4 | MR 0160822 | Zbl 0125.01503
[13] Wang, Y., Miao, L., Gao, Z., Liu, W.: The influence of second maximal subgroups on the generalized $p$-solvability of finite groups. Commun. Algebra 50 (2022), 2584-2591. DOI 10.1080/00927872.2021.2014512 | MR 4413853 | Zbl 1505.20015
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