Displaying similar documents to “Solvable finite groups with a particular configuration of Fitting sets”

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...

On locally finite minimal non-solvable groups

Ahmet Arıkan, Sezgin Sezer, Howard Smith (2010)

Open Mathematics

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In the present work we consider infinite locally finite minimal non-solvable groups, and give certain characterizations. We also define generalizations of the centralizer to establish a result relevant to infinite locally finite minimal non-solvable groups.

Generation of finite groups by nilpotent subgroups

E. Damian (2003)

Bollettino dell'Unione Matematica Italiana

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We study the generation of finite groups by nilpotent subgroups and in particular we investigate the structure of groups which cannot be generated by n nilpotent subgroups and such that every proper quotient can be generated by n nilpotent subgroups. We obtain some results about the structure of these groups and a lower bound for their orders.

6-BFC groups

Cliff David, James Wiegold (2006)

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...