# On minimal non-MSN-groups

## Related Articles

- 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...

- Structure of finite groups with S-quasinormal third maximal subgroups. Lutsenko, Yu. V.; Skiba, A. N. // Ukrainian Mathematical Journal;Dec2009, Vol. 61 Issue 12, p1915
We study finite groups whose 3-maximal subgroups are permutable with all Sylow subgroups.

- ON MINIMAL NON- MSP-GROUPS. Guo, P.; Zhang, X. // Ukrainian Mathematical Journal;Feb2012, Vol. 63 Issue 9, p1458
A finite group G is called an MSP-group if all maximal subgroups of the Sylow subgroups of G are S-quasinormal in G: We give a complete classification of groups that are not MSP-groups but all their proper subgroups are MSP-groups.

- Finite Groups with X-permutable Maximal Subgroups of Sylow Subgroups. Jaraden, Jehad Jumah; Al-Dababseh, Awni Faez // Southeast Asian Bulletin of Mathematics;2007, Vol. 31 Issue 6, p1097
Let A, B be subgroups of a group G and ... â‰ X âŠ† G. Then, A is said to be X-permutable with B [6] if there exists an element x âˆˆ X such that ABx = Bx A. In this paper we study finite groups in which maximal subgroups of Sylow subgroups are X-permutable either with maximal...

- The influence of M-normal subgroups of Sylow subgroups on the structure of finite groups. Zhaonian, P. U.; TANG Juping // Journal of Huazhong Normal University;2013, Vol. 52 Issue 2, p155
A subgroup H of G is said to be M-normal in G if there exists a normal subgroup B of G such that G = HB and H1B

- Finite groups with some maximal subgroups of Sylow subgroups â„³-supplemented. Long Miao // Mathematical Notes;Dec2009, Vol. 86 Issue 5/6, p655
A subgroup H of a group G is said to be â„³-supplemented in G if there exists a subgroup B of G such that G = HB and TB < G for every maximal subgroup T of H. In this paper, we obtain the following statement: Let â„± be a saturated formation containing all supersolvable groups and H be a...

- The Influence of X-s-semipermutable Subgroups on the Structure of Finite Groups. Hao, L. P.; Zhang, X. J.; Yu, Q. // Southeast Asian Bulletin of Mathematics;2009, Vol. 33 Issue 3, p421
Let X be a non-empty subset of a group G. A subgroup A of G is said to be X-s-semipermutable in G if A has a supplement T in G such that for every Sylow subgroup Tp of T, there exists an element x âˆˆ X such that ATpx = Tpx A. In this paper, we use X-s-semipermutable subgroup to determine the...

- Finite solvable groups with C-closed invariant subgroups. Antonov, V.; Chekanov, S. // Mathematical Notes;Jun/Jul2007, Vol. 81 Issue 5/6, p708
The article examines the finite solvable groups in which all normal subgroups are C-closed. It cites that it is easy to see that a subgroup H of a group G is C-closed if H = C(M) for some subset M of G. According to the article, the finite groups in which all subgroups are C-closed. It further...

- Cyclicity conditions for G-chief factors of normal subgroups of a group G. Skiba, A. // Siberian Mathematical Journal;Jan2011, Vol. 52 Issue 1, p127
We find conditions under which every G-chief factor of a normal subgroup E of a finite group G is cyclic.