On groups with many normal subgroups

[1] M. Brescia and A. Russo, On cyclic automorphisms of a group, J. Algebra Appl., 20 (2021) 13 pp.
[2] S. N. Chernikov, On groups with restrictions on subgroups, Naukova Dumka: Kiev, (1971) 17–39.
[3] C. D. H. Cooper, Power automorphisms of a group, Math. Z., 107 (1968) 335–356.
[4] M. R. Dixon and I. Y. Subbotin, Groups with finiteness conditions on some subgroup systems: a contemporary stage, Algebra Discrete Math., 4 (2009) 29–54.
[5] F. de Giovanni, L. A. Kurdachenko and A. Russo, Groups satisfying the miniml condition on subgroups which are not transitively normal, Rend. Circ. Mat. Palermo, 71 (2022) 397–405.
[6] F. de Giovanni, L. A. Kurdachenko and A. Russo, Groups with pronormal deviation, J. Algebra, 613 (2023) 32–45.
[7] F. de Giovanni, L. A. Kurdachenko and A. Russo, Groups with subnormal deviation, Mathematics, 11 (2023) 7 pp.
[8] V. E. Goretsky and L. A. Kurdachenko, The groups with the weak minimal and weak maximal conditions on non-normal subgroups, Ukrain. Math. J., 41 (1989) 1705–1709.
[9] D. J. S. Robinson, Groups in which normality is a transitive relation, Proc. Cambridge Philos. Soc., 60 (1964) 21–38.
[10] D. J. S. Robinson, Finiteness conditions and generalized soluble groups groups, Springer-Verlag, Berlin, 1972.
[11] A. V. Tushev, On deviation in groups, Illinois Math. J. 47 (2003) 539–550.
[12] D. I. Zaitsev, The groups satisfying the weak minimal condition, Ukrain. Math. J., 20 (1968) 472–482.
[13] D. I. Zaitsev, On the theory of minimax groups, Ukrain. Math. J., 23 (1971) 652–660.