Nilpotent Groups
Dailu Li, Xiquan Liang, Yanhong Men (2010)
Formalized Mathematics
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This article describes the concept of the nilpotent group and some properties of the nilpotent groups.
Displaying similar documents to “Note on the -nilpotency in finite groups.”
Nilpotent Groups
OnCSQ-normal subgroups of finite groups
Yong Xu, Xianhua Li (2016)
Open Mathematics
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We introduce a new subgroup embedding property of finite groups called CSQ-normality of subgroups. Using this subgroup property, we determine the structure of finite groups with some CSQ-normal subgroups of Sylow subgroups. As an application of our results, some recent results are generalized.
On subgroups of ZJ type of an F-injector for Fitting classes F between E and ES.
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).
On a theorem of Frobenius.
Bakić, Radoš (1997)
Publications de l'Institut Mathématique. Nouvelle Série
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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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Artinian and noetherian factorized groups
Bernhard Amberg (1976)
Rendiconti del Seminario Matematico della Università di Padova
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Subnormal, permutable, and embedded subgroups in finite groups
James Beidleman, Mathew Ragland (2011)
Open Mathematics
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The purpose of this paper is to study the subgroup embedding properties of S-semipermutability, semipermutability, and seminormality. Here we say H is S-semipermutable (resp. semipermutable) in a group Gif H permutes which each Sylow subgroup (resp. subgroup) of G whose order is relatively prime to that of H. We say H is seminormal in a group G if H is normalized by subgroups of G whose order is relatively prime to that of H. In particular, we establish that a seminormal p-subgroup is...
On a class of finite solvable groups
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...
The -injectors of a finite group
M. J. Iranzo, M. Torres (1989)
Rendiconti del Seminario Matematico della Università di Padova
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Carter subgroups and injectors in a class of locally finite groups
B. Hartley, M. J. Tomkinson (1988)
Rendiconti del Seminario Matematico della Università di Padova
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Groups whose all subgroups are ascendant or self-normalizing
Leonid Kurdachenko, Javier Otal, Alessio Russo, Giovanni Vincenzi (2011)
Open Mathematics
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This paper studies groups G whose all subgroups are either ascendant or self-normalizing. We characterize the structure of such G in case they are locally finite. If G is a hyperabelian group and has the property, we show that every subgroup of G is in fact ascendant provided G is locally nilpotent or non-periodic. We also restrict our study replacing ascendant subgroups by permutable subgroups, which of course are ascendant [Stonehewer S.E., Permutable subgroups of infinite groups,...