THE $c$-SUPPLEMENTED PROPERTY OF FINITE GROUPS

Wei, Hou; Wang, Yanming

doi:10.1017/s0013091504001385

Cited by 12 publications

(3 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By replacing "π-quasinormality" by "cnormality", then "c-supplementation", a lot of authors have obtained many results which are analogous to those mentioned above (see Refs. [4,6,[11][12][13][21][22][23][24]). Here we omit the process, simply skipping to the most recent results.…”

Section: Introduction and Statements Of Resultsmentioning

confidence: 99%

π-quasinormally embedded and c-supplemented subgroup of finite group

Peng

2008

Front. Math. China

View full text Add to dashboard Cite

Section: Introduction and Statements Of Resultsmentioning

confidence: 99%

π-quasinormally embedded and c-supplemented subgroup of finite group

Peng

2008

Front. Math. China

View full text Add to dashboard Cite

“…Suppose that [x, y] = 1. Since x 2 ∈ P ≤ Z(P ) by (3) and 1, we obtain that 1 = [x 2 , y] = [x, y] 2 , and so [x, y] is an involution lying in the center of P . It follows that xy is a real element of order 4 by Lemma D, which is not possible by (4).…”

Section: Vol 113 (2019)mentioning

confidence: 99%

“…Corollary C [3,Lemma 2.3]. Let K be a group of odd order that acts on a quaternion free 2-group P , and assume that K fixes all elements of order 2 in P .…”

Section: Introductionmentioning

confidence: 99%

A short note on Isaacs–Navarro’s Theorem

Kızmaz

2019

Arch. Math.

View full text Add to dashboard Cite

show abstract

Weakly SS-Quasinormal Minimal Subgroups and the Nilpotency of a Finite Group

Ting

Zhang

2014

Ukr Math J

View full text Add to dashboard Cite

A subgroup H is said to be an s-permutable subgroup of a finite group G provided that HP = P H holds for every Sylow subgroup P of G, and H is said to be SS-quasinormal in G if there is a supplement B of H to G such that H permutes with every Sylow subgroup of B. We show that H is weakly SS-quasinormal in G if there exists a normal subgroup T of G such that HT is s-permutable and H ∩ T is SS-quasinormal in G. We investigate the influence of some weakly SS-quasinormal minimal subgroups on the nilpotency of a finite group G. Numerous results known from the literature are unified and generalized. Пiдгрупа H називається s-переставною пiдгрупою скiнченної групи G за умови, що HP = P H виконується для кожної силовської пiдгрупи P групи G; H називається SS-квазiнормальною в G, якщо iснує доповнення B пiдгрупи H до G таке, що H можна переставити з кожною силовською пiдгрупою B. Показано, що H є слабко SS-квазiнормальною в G, якщо iснує нормальна пiдгрупа T групи G така, що HT є s-переставною, а H ∩ T є SS-квазiнормальною в G. Дослiджено вплив деяких слабко SS-квазiнормальних мiнiмальних пiдгруп на нiльпотентнiсть скiнченної групи G. Велику кiлькiсть вiдомих з лiтератури результатiв упорядковано та узагальнено.

show abstract

THE $c$-SUPPLEMENTED PROPERTY OF FINITE GROUPS

Abstract: The purpose of this paper is to study the influence of c-supplemented minimal subgroups on the p-nilpotency of finite groups. We obtain 'iff' and 'localized' versions of theorems of Itô and Buckley on nilpotence, p-nilpotence and supersolvability.

Cited by 12 publications

References 24 publications

π-quasinormally embedded and c-supplemented subgroup of finite group

π-quasinormally embedded and c-supplemented subgroup of finite group

A short note on Isaacs–Navarro’s Theorem

Weakly SS-Quasinormal Minimal Subgroups and the Nilpotency of a Finite Group

Contact Info

Product

Resources

About