scholarly journals The fundamental group of quotients of products of some topological spaces by a finite group - A generalization of a Theorem of Bauer-Catanese-Grunewald-Pignatelli: Le groupe fondamental de quotients de produits de certains espaces topologiques par ungroupe fini — Généralisation d’un théorème de Bauer–Catanese–Grunewald–Pignatelli

2021 ◽  
Vol Volume 5 ◽  
Author(s):  
Rodolfo Aguilar
Keyword(s):  
Finite Group ◽  
Finite Number ◽  
Fundamental Group ◽  
Universal Cover ◽  
Connected Components ◽  
Topological Spaces ◽  
Group A ◽  
A Finite Group ◽  
Path Connected

We provide a description of the fundamental group of the quotient of a product of topological spaces X i, each admitting a universal cover, by a finite group G, provided that there is only a finite number of path-connected components in X g i for every g ∈ G. This generalizes previous work of Bauer-Catanese-Grunewald-Pignatelli and Dedieu-Perroni. Nous fournissons une description du groupe fondamental du quotient d’un produitd’espaces topologiques Xi , chacun admettant un revêtement universel, par un groupe fini G,pourvu qu’il n’existe qu’un nombre ni de composantes connexes par arcs dans Xgi pour chaque g ∈ G. Cela généralise des résultats antérieurs de Bauer–Catanese–Grunewald–Pignatelli et deDedieu–Perroni.

scholarly journals Finite Groups with Certain Permutability Criteria

2019 ◽  
Vol 12 (2) ◽  
pp. 571-576 ◽  
Author(s):  
Rola A. Hijazi ◽  
Fatme M. Charaf
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Sylow Subgroups ◽  
Group A ◽  
A Finite Group

Let G be a finite group. A subgroup H of G is said to be S-permutable in G if itpermutes with all Sylow subgroups of G. In this note we prove that if P, the Sylowp-subgroup of G (p > 2), has a subgroup D such that 1 <|D|<|P| and all subgroups H of P with |H| = |D| are S-permutable in G, then G′ is p-nilpotent.

On Conjugate-Permutable Subgroups of a Finite Group

2005 ◽  
Vol 12 (04) ◽  
pp. 669-676 ◽  
Author(s):  
Mingyao Xu ◽  
Qinhai Zhang
Keyword(s):  
Finite Group ◽  
Necessary Conditions ◽  
Permutable Subgroups ◽  
Group A ◽  
A Finite Group

Let G be a finite group. A subgroup H of G is called conjugate-permutable in G if HHg = HgH for any g ∈ G. A group G is called an ECP-group if every subgroup of G is conjugate-permutable in G. In this paper, we study the influence of conjugate-permutable subgroups on the structure of a finite group, especially on the nilpotency or supersolvability of the group, and give some sufficient or necessary conditions for a finite group to be an ECP-group.

On SS-supplemented subgroups of some sylow subgroups of finite groups

2021 ◽  
Author(s):  
Xuanli He ◽  
Qinghong Guo ◽  
Muhong Huang
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Necessary Conditions ◽  
Saturated Formation ◽  
Sylow Subgroups ◽  
Group A ◽  
Sufficient And Necessary Conditions ◽  
A Finite Group

Let [Formula: see text] be a finite group. A subgroup [Formula: see text] of [Formula: see text] is called to be [Formula: see text]-permutable in [Formula: see text] if [Formula: see text] permutes with all Sylow subgroups of [Formula: see text]. A subgroup [Formula: see text] of [Formula: see text] is said to be [Formula: see text]-supplemented in [Formula: see text] if there exists a subgroup [Formula: see text] of [Formula: see text] such that [Formula: see text] and [Formula: see text] is [Formula: see text]-permutable in [Formula: see text]. In this paper, we investigate [Formula: see text]-nilpotency of a finite group. As applications, we give some sufficient and necessary conditions for a finite group belongs to a saturated formation.

A new characterization of Suzuki’s simple groups

2017 ◽  
Vol 16 (11) ◽  
pp. 1750216 ◽  
Author(s):  
Jinshan Zhang ◽  
Changguo Shao ◽  
Zhencai Shen
Keyword(s):  
Finite Group ◽  
Character Formula ◽  
Simple Groups ◽  
Complex Character ◽  
Group A ◽  
Vanishing Elements ◽  
A Finite Group

Let [Formula: see text] be a finite group. A vanishing element of [Formula: see text] is an element [Formula: see text] such that [Formula: see text] for some irreducible complex character [Formula: see text] of [Formula: see text]. Denote by Vo[Formula: see text] the set of the orders of vanishing elements of [Formula: see text]. In this paper, we prove that if [Formula: see text] is a finite group such that Vo[Formula: see text], [Formula: see text], then [Formula: see text].

ON THE POSET OF NON-TRIVIAL PROPER SUBGROUPS OF A FINITE GROUP

2003 ◽  
Vol 02 (02) ◽  
pp. 165-168 ◽  
Author(s):  
MARIA SILVIA LUCIDO
Keyword(s):  
Finite Group ◽  
Partially Ordered Set ◽  
Ordered Set ◽  
Connected Components ◽  
Partially Ordered ◽  
Simple Connectivity ◽  
A Finite Group

In this paper we describe the connected components of ℒ(G), the partially ordered set of non-trivial proper subgroups of a finite group G. This result is related to the study of the simple connectivity of the coset poset of a finite group.

The Influence of Certain Abelian Subgroups on the Structure of Finite Groups

2008 ◽  
Vol 15 (03) ◽  
pp. 479-484 ◽  
Author(s):  
M. Ramadan
Keyword(s):  
Finite Group ◽  
Finite Groups ◽  
Prime Power ◽  
Prime Power Order ◽  
Group A ◽  
Abelian Subgroups ◽  
A Finite Group

Let G be a finite group. A subgroup K of a group G is called an [Formula: see text]-subgroup of G if NG(K) ∩ Kx ≤ K for all x ∈ G. The set of all [Formula: see text]-subgroups of G is denoted by [Formula: see text]. In this paper, we investigate the structure of a group G under the assumption that certain abelian subgroups of prime power order belong to [Formula: see text].

A classification of groups with a centralizer condition

1976 ◽  
Vol 15 (1) ◽  
pp. 81-85 ◽  
Author(s):  
Zvi Arad ◽  
Marcel Herzog
Keyword(s):  
Finite Group ◽  
Simple Groups ◽  
Group A ◽  
Nontrivial Subgroup ◽  
A Finite Group

Let G be a finite group. A nontrivial subgroup M of G is called a CC-subgroup if M contains the centralizer in G of each of its nonidentity elements. The purpose of this paper is to classify groups with a CC-subgroup of order divisible by 3. Simple groups satisfying that condition are completely determined.

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