Let G be a finite group and H a subgroup of G. We say that H has an IC-property if the intersection of H and [H,G] satisfy some conditions. In this paper, we investigate the structure of a finite group G under the assumption that some maximal subgroups, 2-maximal subgroups, 3-maximal subgroups of G have the ICp-property and obtain some new characterizations of p-solvable and solvable groups.
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Gao et al. (2024) studied this question.