Groups with the Minimal Condition on Non-“Nilpotent-by-Finite” Subgroups

Let U(RG) be the unit group of the group ring RG. Groups G such that U(RG) is FC-nilpotent are determined, where R is the ring of integers Z or a field K of characteristic zero.

Soluble products of nilpotent groups

John C. Lennox, Derek J. S. Robinson (1980)

Rendiconti del Seminario Matematico della Università di Padova

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On maximal subgroups of minimax groups

Silvana Franciosi, Francesco de Giovanni (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

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It is proved that a soluble residually finite minimax group is finite-by-nilpotent if and only if it has only finitely many maximal subgroups which are not normal.

On finite soluble groups verifying an extremal condition on subgroups.

Fernando Tuccillo (1991)

Collectanea Mathematica

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We classify the finite soluble groups satisfying the following condition: if H is a subgroup of G and H is not nilpotent, then the Fitting subgroup of H is the centralizer in H of its derived subgroup H'.