Displaying similar documents to “On the Structure of the Normal Subgroups of a Group: Nilpotency.”

Groups with Restricted Conjugacy Classes

de Giovanni, F., Russo, A., Vincenzi, G. (2002)

Serdica Mathematical Journal

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Let F C 0 be the class of all finite groups, and for each nonnegative integer n define by induction the group class FC^(n+1) consisting of all groups G such that for every element x the factor group G/CG ( <x>^G ) has the property FC^n . Thus FC^1 -groups are precisely groups with finite conjugacy classes, and the class FC^n obviously contains all finite groups and all nilpotent groups with class at most n. In this paper the known theory of FC-groups is taken as a model, and it...

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,...

Maximal subgroups and PST-groups

Adolfo Ballester-Bolinches, James Beidleman, Ramón Esteban-Romero, Vicent Pérez-Calabuig (2013)

Open Mathematics

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A subgroup H of a group G is said to permute with a subgroup K of G if HK is a subgroup of G. H is said to be permutable (resp. S-permutable) if it permutes with all the subgroups (resp. Sylow subgroups) of G. Finite groups in which permutability (resp. S-permutability) is a transitive relation are called PT-groups (resp. PST-groups). PT-, PST- and T-groups, or groups in which normality is transitive, have been extensively studied and characterised. Kaplan [Kaplan G., On T-groups, supersolvable...

On some properties of pronormal subgroups

Leonid Kurdachenko, Alexsandr Pypka, Igor Subbotin (2010)

Open Mathematics

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New results on tight connections among pronormal, abnormal and contranormal subgroups of a group have been established. In particular, new characteristics of pronormal and abnormal subgroups have been obtained.

Algorithms for permutability in finite groups

Adolfo Ballester-Bolinches, Enric Cosme-Llópez, Ramón Esteban-Romero (2013)

Open Mathematics

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In this paper we describe some algorithms to identify permutable and Sylow-permutable subgroups of finite groups, Dedekind and Iwasawa finite groups, and finite T-groups (groups in which normality is transitive), PT-groups (groups in which permutability is transitive), and PST-groups (groups in which Sylow permutability is transitive). These algorithms have been implemented in a package for the computer algebra system GAP.