scholarly journals Groups with a Cyclic Sylow Subgroup

1966 ◽  
Vol 27 (2) ◽  
pp. 571-584 ◽  
Author(s):  
Walter Feit
Keyword(s):  
Sylow Subgroup ◽  
Prime Order ◽  
Modular Representations ◽  
Sylow Group

By focussing attention on indecomposable modular representations J. G. Thompson [11] has recently simplified and generalized some classical results of R. Brauer [1] concerning groups which have a Sylow group of prime order. In this paper this approach will be used to prove some results which generalize theorems of R. Brauer [2] and H. F. Tuan [12].

Finite Groups with Certain S-Permutable and GS-Maximal Subgroups

2020 ◽  
Vol 27 (04) ◽  
pp. 661-668
Author(s):  
A.M. Elkholy ◽  
M.H. Abd-Ellatif
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sylow Subgroup ◽  
Prime Order ◽  
Maximal Subgroups ◽  
A Finite Group

Let G be a finite group and H a subgroup of G. We say that H is S-permutable in G if H permutes with every Sylow subgroup of G. A group G is called a generalized smooth group (GS-group) if [G/L] is totally smooth for every subgroup L of G of prime order. In this paper, we investigate the structure of G under the assumption that each subgroup of prime order is S-permutable if the maximal subgroups of G are GS-groups.

On the supersolubility of a group with some tcc-subgroups

2019 ◽  
pp. 2150020
Author(s):  
Alexander Trofimuk
Keyword(s):  
Sylow Subgroup ◽  
Prime Order ◽  
Maximal Subgroups ◽  
Sylow Subgroups

A subgroup [Formula: see text] of a group [Formula: see text] is called tcc-subgroup in [Formula: see text], if there is a subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and for any [Formula: see text] and for any [Formula: see text], there exists an element [Formula: see text] such that [Formula: see text]. The notation [Formula: see text] means that [Formula: see text] is a subgroup of a group [Formula: see text]. In this paper, we proved the supersolubility of a group [Formula: see text] in the following cases: [Formula: see text] and [Formula: see text] are supersoluble tcc-subgroups in [Formula: see text]; all Sylow subgroups of [Formula: see text] and of [Formula: see text] are tcc-subgroups in [Formula: see text]; all maximal subgroups of [Formula: see text] and of [Formula: see text] are tcc-subgroups in [Formula: see text]. Besides, the supersolubility of a group [Formula: see text] is obtained in each of the following cases: all maximal subgroups of every Sylow subgroup of [Formula: see text] are tcc-subgroups in [Formula: see text]; every subgroup of prime order or 4 is a tcc-subgroup in [Formula: see text]; all 2-maximal subgroups of [Formula: see text] are tcc-subgroups in [Formula: see text].

scholarly journals ON MINIMAL SUBGROUPS OF FINITE GROUPS

2009 ◽  
Vol 51 (2) ◽  
pp. 359-366 ◽  
Author(s):  
M. ASAAD
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sylow Subgroup ◽  
Prime Order ◽  
Minimal Subgroup ◽  
Minimal Subgroups ◽  
Group A ◽  
A Finite Group

AbstractLet G be a finite group. A minimal subgroup of G is a subgroup of prime order. A subgroup of G is called S-quasinormal in G if it permutes with each Sylow subgroup of G. A group G is called an MS-group if each minimal subgroup of G is S-quasinormal in G. In this paper, we investigate the structure of minimal non-MS-groups (non-MS-groups all of whose proper subgroups are MS-groups).

Functional encryption for computational hiding in prime order groups via pair encodings

2017 ◽  
Vol 86 (1) ◽  
pp. 97-120 ◽  
Author(s):  
Jongkil Kim ◽  
Willy Susilo ◽  
Fuchun Guo ◽  
Man Ho Au
Keyword(s):  
Prime Order ◽  
Functional Encryption
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