# A Generalization of c-Supplementation

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The finite groups containing exactly two noncomplemented subgroups are described.

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The solvability of any finite group with Hall supplements to normalizers of the Sylow subgroups is established.

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We study finite groups whose 3-maximal subgroups are permutable with all Sylow subgroups.

- 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©...

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The normalizer of each Sylow subgroup of a finite group G has a nilpotent Hall supplement in G if and only if G is soluble and every tri-primary Hall subgroup H (if exists) of G satisfies either of the following two statements: (i) H has a nilpotent bi-primary Hall subgroup; (ii) Let Ï€( H) =...

- A condition for the solvability of finite groups. Miao, Long; Qian, Guohua // Siberian Mathematical Journal;Jul2009, Vol. 50 Issue 4, p687
A subgroup H is called â„³-supplemented in a finite group G, if there exists a subgroup B of G such that G = HB and H1 B is a proper subgroup of G for every maximal subgroup H1 of H. We investigate the influence of â„³-supplementation of Sylow subgroups and obtain a condition for...

- On Weakly s-supplemented Subgroups of Finite Groups. Yujian Huang; Yangming Liy // Southeast Asian Bulletin of Mathematics;2009, Vol. 33 Issue 3, p443
Let G be a finite group and H a subgroup of G. Then H is said to be s-permutable in G if HGp = GpH for any Sylow p-subgroup Gp of G; H is said to be weakly s-supplemented subgroup of G if there is a subgroup T of G such that G = HT and H âˆ© T â‰¤ HsG, where HsG is the subgroup of H...

- A Characterization Of Some Linear Groups By The Number Of Sylow Subgroups. Asboei, Alireza Khalili; Amiri, Seyed Sadegh Salehi; Iranmanesh, Ali; Tehranian, Abolfazl // Australian Journal of Basic & Applied Sciences;2011, Vol. 5 Issue 9, p831
Let G be a finite group with trivial center and np(G) be the number of Sylow p-subgroup of G. In this paper we prove that if np(G)= np(PSL(2, q)), for every prime p âˆŠ Ï€(G), where q âˆŠ{16, 17, 19, 23}. Then if q âˆŠ{16, 19}, G â‰… PSL(2, q) and if qâˆŠ{17, 23, 25}, PSL(2,...

- Finite groups in which the normalizers of Sylow 3-subgroups are of odd or primary index. Kondrat'ev, A. S.; Guo, W. // Siberian Mathematical Journal;Mar2009, Vol. 50 Issue 2, p272
We determine the composition factors of the finite groups in which the normalizers of Sylow 3-subgroups are of odd or primary index.