On NR*-subgroups of finite groups

Xianggui ZHONG
March 2014
Turkish Journal of Mathematics;Mar2014, Vol. 38 Issue 2, p240
Academic Journal
Let G be a finite group and let H be a subgroup of G. H is said to be an NR*-subgroup of G if there exists a normal subgroup T of G such that G = HT and if whenever K ◁ H and g ∈ G, then Kg ∩ H ∩ T ≤ K. A number of new characterizations of a group G are given, under the assumption that all Sylow subgroups of certain subgroups of G are N*-subgroups.


Related Articles

  • A NOTE ON RESIDUALS IN GROUPS WITH QUASICENTRAL ABELIAN NORMAL SUBGROUPS. Kurdachenko, L. A.; Subbotin, I. Ya. // Serdica Mathematical Journal;2016, Vol. 42 Issue 3/4, p325 

    In 1973, I. N. AbramovskiÄ­ initiated the study of groups in which the transitivity condition is imposed on abelian normal subgroups only. He studied these locally finite groups under the additional restriction of commutativity of their Sylow p-subgroups. Much later the groups in which all...

  • Several Kinds of Special Solvable Groups. Jiechun Hu; Guiyun Chen // Southeast Asian Bulletin of Mathematics;2011, Vol. 35 Issue 4, p617 

    It is a well-known fact that subgroups of a group can give information of whole group, especially normal subgroups in a group greatly influence on the structure of the group. For example, a nilpotent group is a direct product of Sylow subgroups; a solvable group is a group with a normal series...

  • Structure of a group with elements of order at most 4. Lytkina, D. V. // Siberian Mathematical Journal;Mar2007, Vol. 48 Issue 2, p283 

    We prove that every group in which the order of each element is at most 4 either possesses a nontrivial class 2 nilpotent normal Sylow subgroup or includes a normal elementary abelian 2-subgroup the quotient by which is isomorphic to the nonabelian group of order 6.

  • Structure of solvable rational groups. Hegedus Pl // Proceedings of the London Mathematical Society;Mar2005, Vol. 90 Issue 2, p439 

    R. Gow proved that the order of a solvable rational group is divisible only by the primes 2, 3 and 5. In this paper it is proved that in a solvable rational group the Sylow 5-subgroup is always normal and elementary Abelian. Moreover, the structure of rational {2, 5}-groups is described in detail.

  • On rationality and 2-reflexiveness of wreath products of finite groups. Kolesnikov, S. // Mathematical Notes;Sep/Oct2006, Vol. 80 Issue 3/4, p380 

    A finite group G is said to be rational if each its irreducible character acquires only rational values, and it is said to be 2- reflexive if each its element can be represented as a product of at most two involutions. We find necessary and sufficient conditions for the wreath of two finite...

  • On the Sylow Normalizers of Some Simple Classical Groups. AHANJIDEH, N.; IRANMANESH, A. // Bulletin of the Malaysian Mathematical Sciences Society;2012, Vol. 35 Issue 2, p459 

    Let G be a finite group and π(G) be the set of prime divisors of the order of G. For t ϵ π(G) denote by nt (G) the order of a normalizer of t-Sylow subgroup of G and put n(G) = {nt (G) : t ϵ π(G)}. In this paper, we give an answer to the following problem, for the groups of Lie...

  • On the Solvability of Finite Irreducible Linear Groups with Hall TI-Subgroups. Bobr, V.V. // Mathematical Notes;Mar/Apr2003, Vol. 73 Issue 3/4, p467 

    Conditions for a π-solvable complex linear group of a relatively small degree to be solvable are found.

  • 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 ℱ be a class of groups and let G be a finite group. We call a set Σ of subgroups of G a covering subgroup system of G for ℱ (or directly an ℱ-covering subgroup system of G) if G ∈ ℱ whenever every subgroup in Σ is in ℱ. 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...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics