A -theorem for -injectors in finite groups
M. J. Iranzo, A. Martínez-Pastor, F. Pérez-Monasor (1992)
Rendiconti del Seminario Matematico della Università di Padova
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M. J. Iranzo, A. Martínez-Pastor, F. Pérez-Monasor (1992)
Rendiconti del Seminario Matematico della Università di Padova
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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'.
Bakić, Radoš (2004)
Novi Sad Journal of Mathematics
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Ana Martínez Pastor (1994)
Publicacions Matemàtiques
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Let G be a finite group and p a prime. We consider an F-injector K of G, being F a Fitting class between E y ES, and we study the structure and normality in G of the subgroups ZJ(K) and ZJ*(K), provided that G verifies certain conditions, extending some results of G. Glauberman (A characteristic subgroup of a p-stable group, (1968), 555-564).
Artemovych, O. (2002)
Serdica Mathematical Journal
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We characterize the groups which do not have non-trivial perfect sections and such that any strictly descending chain of non-“nilpotent-by-finite” subgroups is finite.
Markku Niemenmaa, Miikka Rytty (2008)
Commentationes Mathematicae Universitatis Carolinae
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In this paper we consider finite loops whose inner mapping groups are nilpotent. We first consider the case where the inner mapping group of a loop is the direct product of a dihedral group of order and an abelian group. Our second result deals with the case where is a -loop and is a nilpotent group whose nonabelian Sylow subgroups satisfy a special condition. In both cases it turns out that is centrally nilpotent.
James Beidleman, Hermann Heineken, Jack Schmidt (2013)
Open Mathematics
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A finite solvable group G is called an X-group if the subnormal subgroups of G permute with all the system normalizers of G. It is our purpose here to determine some of the properties of X-groups. Subgroups and quotient groups of X-groups are X-groups. Let M and N be normal subgroups of a group G of relatively prime order. If G/M and G/N are X-groups, then G is also an X-group. Let the nilpotent residual L of G be abelian. Then G is an X-group if and only if G acts by conjugation on...
Bernhard Amberg (1976)
Rendiconti del Seminario Matematico della Università di Padova
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