Displaying similar documents to “Finite groups whose set of numbers of subgroups of possible order has exactly 2 elements”

On S -quasinormal and c -normal subgroups of a finite group

Shirong Li, Yangming Li (2008)

Czechoslovak Mathematical Journal

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Let ℱ be a saturated formation containing the class of supersolvable groups and let G be a finite group. The following theorems are presented: (1) G ∈ ℱ if and only if there is a normal subgroup H such that G / H ∈ ℱ and every maximal subgroup of all Sylow subgroups of H is either c -normal or S -quasinormally embedded in G . (2) G ∈ ℱ if and only if there is a normal subgroup H such that G / H ∈ ℱ and every maximal subgroup of all Sylow subgroups of F * ( H ) , the generalized Fitting subgroup of H , is either c -normal...

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.

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,...

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...