On finite groups with given ICΦ-subgroups
Research output: Contribution to journal › Research article › Contributed › peer-review
Contributors
Abstract
A subgroup H of a group G is said to be an ICΦ-subgroup of G if H ∩ [H, G] ≤ Φ(H). We analyze the structure of a finite group G under the assumption that some given subgroups of G are ICΦ-subgroups of G. A new characterization of finite abelian groups and some new criteria for 2-nilpotence and nilpotence of finite groups will be obtained. Moreover, we will obtain two criteria for a finite group to lie in a given solvably saturated formation containing the class of finite supersolvable groups.
Details
Original language | English |
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Article number | 2450016 |
Journal | Journal of algebra and its applications : JAA |
Volume | 23 |
Issue number | 1 |
Publication status | Published - 1 Jan 2024 |
Peer-reviewed | Yes |
Keywords
ASJC Scopus subject areas
Keywords
- 2-maximal subgroups, 2-nilpotent, 3-maximal subgroups, abelian, Finite groups, ICΦ-subgroups, maximal subgroups, nilpotent, solvably saturated formations