# On Sylow Subgroups of Some Shunkov Groups

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- c*-Quasinormally embedded subgroups of finite groups. Li, Changwen; Huang, Jianhong; Hu, Bin // Frontiers of Mathematics in China;Aug2012, Vol. 7 Issue 4, p703
Suppose that G is a finite group and H is a subgroup of G. H is said to be s-quasinormally embedded in G if for each prime p dividing | H|, a Sylow p-subgroup of H is also a Sylow p-subgroup of some s-quasinormal subgroup of G; H is called c*-quasinormally embedded in G if there is a subgroup T...

- A covering subgroup system for the class of p-nilpotent groups. Huang, J.; Yang, N.; Hu, B.; Yu, X. // Siberian Mathematical Journal;Mar2012, Vol. 53 Issue 2, p352
Let â„± be a class of groups and let G be a finite group. We call a set Î£ of subgroups of G a covering subgroup system of G for â„± (or directly an â„±-covering subgroup system of G) if G âˆˆ â„± whenever every subgroup in Î£ is in â„±. We give some covering subgroup...

- On X-ss-permutable Subgroups of Finite Groups. Feng Peng; Shirong Li; Kun Li; Yanru Bai // Southeast Asian Bulletin of Mathematics;2011, Vol. 35 Issue 2, p285
In this paper, the following concept is introduced: A subgroup H of G is said to be X-ss-permutable in G if there is a nonempty subset X of G and H is X-permutable with all Sylow subgroups of some supplement T of H to G. In this paper, groups with certain X-ss-permutable subgroups of prime power...

- A new characterization of L( r) by their Sylow numbers. Asboei, Alireza // Acta Mathematica Sinica;Oct2015, Vol. 31 Issue 10, p1593
Let G be a finite centerless group, let Ï€( G) be the set of prime divisors of the order of G, and let n( G) be the number of Sylow p-subgroups of G, that is, n( G) = |Syl( G)|. Set NS( G):= { n( G)| p âˆˆ Ï€( G)}. In this paper, we are investigating whether L( r) is determined up to...

- On weakly Ï„-quasinormal subgroups of finite groups. Lukyanenko, V.; Skiba, A. // Acta Mathematica Hungarica;Nov2009, Vol. 125 Issue 3, p237
Let G be a finite group and H a subgroup of G. We say that: (1) H is Ï„-quasinormal in G if H permutes with all Sylow subgroups Q of G such that (| Q|, | H|) = 1 and (| H|, | Q G|) â‰ 1; (2) H is weakly Ï„-quasinormal in G if G has a subnormal subgroup T such that HT = G and T âˆ©...

- On the finite groups whose Sylow 3-subgroup normalizes a Sylow 3â€²-subgroup. Pal'chik, E. // Siberian Mathematical Journal;Jan2015, Vol. 56 Issue 1, p132
We determine the possible composition factors of finite groups in which the index of the normalizer of a Sylow 3-subgroup is not divisible by a prime s > 3.

- Finite groups with submodular sylow subgroups. Vasilyev, V. // Siberian Mathematical Journal;Nov2015, Vol. 56 Issue 6, p1019
A subgroup H of a finite group G is submodular in G if H can be joined with G by a chain of subgroups each of which is modular in the subsequent subgroup. We reveal some properties of groups with submodular Sylow subgroups. A group G is called strongly supersoluble if G is supersoluble and every...

- Finite groups with S-quasinormally embedded or SS-quasinormal subgroups. Kong, Qingjun // Acta Mathematica Hungarica;Apr2014, Vol. 142 Issue 2, p459
Suppose that G is a finite group and H is a subgroup of G. H is said to be S-quasinormally embedded in G if for each prime p dividing the order of H, a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G; H is said to be an SS-quasinormal subgroup of G if there...

- SUPERSOLUBLE CONDITIONS AND TRANSFER CONTROL. GILOTTI, A. L.; SERENA, L. // International Journal of Group Theory;Mar2013, Vol. 2 Issue 1, p157
In this paper we give a new condition for a Sylow p-subgroup of a finite group to control transfer. Then it is deduced a characterization of supersoluble groups that can be seen as a generalization of the well known result concerning the supersolubility of finite groups with cyclic Sylow...