Corrigendum: Some characterizations of finite groups in which semipermutability is a transitive relation [Forum Math. 22 (2010), 855–862]

2012 ◽  
Vol 24 (6) ◽  
Author(s):  
Kahled A. Al-Sharo ◽  
James C. Beidleman ◽  
Hermann Heineken ◽  
Matthew F. Ragland
Keyword(s):  
Finite Groups ◽  
Transitive Relation

Finite groups in which normality is a transitive relation

2001 ◽  
Vol 76 (5) ◽  
pp. 321-325 ◽  
Author(s):  
M. Asaad ◽  
A.A. Heliel
Keyword(s):  
Finite Groups ◽  
Transitive Relation

scholarly journals Finite groups in which some property of two-generator subgroups is transitive

2007 ◽  
Vol 75 (2) ◽  
pp. 313-320 ◽  
Author(s):  
Costantino Delizia ◽  
Primoz Moravec ◽  
Chiara Nicotera
Keyword(s):  
Finite Groups ◽  
Transitive Group ◽  
Transitive Relation ◽  
Transitive Groups

Finite groups in which a given property of two-generator subgroups is a transitive relation are investigated. We obtain a description of such groups and prove in particular that every finite soluble-transitive group is soluble. A classification of finite nilpotent-transitive groups is also obtained.

Groups in which normality is a weakly transitive relation

2014 ◽  
Vol 14 (01) ◽  
pp. 1550007 ◽  
Author(s):  
Emanuela Romano ◽  
Giovanni Vincenzi
Keyword(s):  
Large Class ◽  
Finite Groups ◽  
Study Groups ◽  
Normal Subgroups ◽  
Transitive Relation ◽  
Weak Transitivity

We study groups in which normality is a weakly transitive relation, giving an extension of in Theorem A [On finite T-groups, J. Aust. Math. Soc. 75 (2003) 181–191] due to Ballester-Bolinches and Esteban-Romero pointing out the relations between these groups and those in which all subgroups are almost pronormal. Moreover, we extend a well-known theorem of Peng [Finite groups with pro-normal subgroups, Proc. Amer. Math. Soc. 20 (1969) 232–234] proving that for a large class of generalized FC-groups the weak transitivity of normality is equivalent to having finitely many maximal pronormalizers of subgroups.

scholarly journals On finite J-groups

2003 ◽  
Vol 75 (2) ◽  
pp. 181-192 ◽  
Author(s):  
A. Ballester-Bolinches ◽  
R. Esteban-Romero
Keyword(s):  
Finite Groups ◽  
Transitive Relation

AbstractCharacterisations of finite groups in which normality is a transitive relation are presented in the paper. We also characterise the finite groups in which every subgroup is either permutable or coincides with its permutiser as the groups in which every subgroup is permutable.

scholarly journals Finite Groups in which SS-Permutability is a Transitive Relation

2014 ◽  
Vol 143 (2) ◽  
pp. 466-479 ◽  
Author(s):  
X. Y. Chen ◽  
W. B. Guo
Keyword(s):  
Finite Groups ◽  
Transitive Relation

scholarly journals A note on finite groups in which C-normality is a transitive relation

2013 ◽  
Vol 8 ◽  
pp. 1881-1887 ◽  
Author(s):  
Doaa Mustafa AlSharo ◽  
Hajar Sulaiman ◽  
Khaled Ahmad AlSharo ◽  
Ibrahim Sulieman
Keyword(s):  
Finite Groups ◽  
Transitive Relation

scholarly journals A generalization to Sylow permutability of pronormal subgroups of finite groups

2019 ◽  
Vol 19 (03) ◽  
pp. 2050052
Author(s):  
R. Esteban-Romero ◽  
P. Longobardi ◽  
M. Maj
Keyword(s):  
Finite Groups ◽  
Transitive Relation ◽  
Or Groups

In this note, we present a new subgroup embedding property that can be considered as an analogue of pronormality in the scope of permutability and Sylow permutability in finite groups. We prove that finite PST-groups, or groups in which Sylow permutability is a transitive relation, can be characterized in terms of this property, in a similar way as T-groups, or groups in which normality is transitive, can be characterized in terms of pronormality.

scholarly journals ON GENERALISED PRONORMAL SUBGROUPS OF FINITE GROUPS

2014 ◽  
Vol 56 (3) ◽  
pp. 691-703 ◽  
Author(s):  
A. BALLESTER-BOLINCHES ◽  
J. C. BEIDLEMAN ◽  
A. D. FELDMAN ◽  
M. F. RAGLAND
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Subnormal Subgroup ◽  
Normal Subgroups ◽  
Transitive Relation ◽  
Formula Group ◽  
Permutable Subgroups ◽  
Sylow Permutable ◽  
A Finite Group ◽  
Subnormal Subgroups

AbstractFor a formation $\mathfrak F$, a subgroup M of a finite group G is said to be $\mathfrak F$-pronormal in G if for each g ∈ G, there exists x ∈ 〈U,Ug〉$\mathfrak F$ such that Ux = Ug. Let f be a subgroup embedding functor such that f(G) contains the set of normal subgroups of G and is contained in the set of Sylow-permutable subgroups of G for every finite group G. Given such an f, let fT denote the class of finite groups in which f(G) is the set of subnormal subgroups of G; this is the class of all finite groups G in which to be in f(G) is a transitive relation in G. A subgroup M of a finite group G is said to be $\mathfrak F$-normal in G if G/CoreG(M) belongs to $\mathfrak F$. A subgroup U of a finite group G is called K-$\mathfrak F$-subnormal in G if either U = G or there exist subgroups U = U0 ≤ U1 ≤ . . . ≤ Un = G such that Ui–1 is either normal or $\mathfrak F$-normal in Ui, for i = 1,2, …, n. We call a finite group G an $fT_{\mathfrak F}$-group if every K-$\mathfrak F$-subnormal subgroup of G is in f(G). In this paper, we analyse for certain formations $\mathfrak F$ the structure of $fT_{\mathfrak F}$-groups. We pay special attention to the $\mathfrak F$-pronormal subgroups in this analysis.

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