关于有限群的Pronormal极小子群

利用有限群G的pronormal极小子群和Sylow子群正规化子中的素数阶弱左Engel元素得到了G成为p-幂零群、幂零群和超可解群的一些充分条件,这些结果推广了已知结论。     

A New Type of Pronormal Subgroups in Chevalley Groups

Let L be a simple Lie algebra with irreducible root system φ having roots of different length,F be a field of characteristic different from 2,G=L(F) be a Chevalley group of type L over F.Denote by φ^1 the set of all long roots in φ.Set G^1=(zr(t);r∈φ^t,t∈F).It is a subgroup of G generated by all the long root subgroups.This paper determines the pronormality of G^1 in G when L is not of type G2.     

关于有限群的$CAP$-嵌入子群

A subgroup H of a finite group G is said to be CAP-embedded subgroup of G if, for each prime p dividing the order of H, there exists a CAP-subgroup K of G such that a Sylow p-subgroup of H is also a Sylow p-subgroup of K. In this paper some new results are obtained based on the assumption that some subgroups of prime power order have the CAP-embedded property in the group.     

Finite Sylow Subgroups in Simple Locally Finite Groups of Lie Type

The main result of the paper is the followingTheorem. Let S = {r₀, r₁, ..., r_n} be a finite nonempty set of primes and let L be a Lie type of Chevalley groups. Then there exists a locally finite field F of characteristic r₀ such that Sylow r-subgroups of the simple group L(F) of type L over F are finite if and only if r ? S.     

On Fisher Subgroups of Finite Groups

Ukrainian Mathematical Journal - Let ? be a Fitting set of a group G, let π be a nonempty set of primes, and let L ≤ G. In this case, ? is called a Fischer π-set of G if...     

On SQ-Supplemented Subgroups of Finite Groups

Let G be a finite group and H ≤ G. The subgroup H is called: S-permutable in G if HP = PH for all Sylow subgroups P of G; S-permutably embedded in G if each Sylow subgroup of H is also a Sylow subgroup of some S-permutable subgroup of G.

Let H be a subgroup of a group G. Then we say that H is SQ-supplemented in G if G has a subgroup T and an S-permutably embedded subgroup C ≤ H such that HT = G and T ∩ H ≤ C.

We study the structure of G under the assumption that some subgroups of G are SQ-supplemented in G. Some known results are generalized.     

On Complemented Subgroups of Finite Groups

51. IntroductionIt is quite clear that the ekistence of complements for some families of subgroups of agroup gives a lot ofinfor~ion about its structure. FOr instance, Hall[6] proved that a groupG is supersoluble with elementary abelian Sylow subgroups if and only if G is complemellted,that is, every subgroup of G is comPlemeded in G. The same anchor also proved that agroup is soluble if and only if every Sylow subgroup is complemellted (see [3;I,3.5]). Morerecelltly, Arad and Wardll] pro…     

On c-Normal Subgroups of Finite Groups

A subgroup H is said to be c-normal in a group G if there exists a normal subgroup K of G such that G = HK and H K is contained in H_G, where H_G is the maximal normal subgroup of G. We determine the structures of some groups in which some primary subgroups is c-normal.AMS Mathematics Subject Classification (2000) 20D10 20D20     

On c-Normal Subgroups of Finite Groups

Let G be a finite group. We fix in every noncyclic Sylow subgroup P of G some subgroup D satisfying 1 < |D| < |P| and study the structure of G under the assumption that all subgroups H of P with |H| = |D| are c-normal in G.     

关于有限群的S-半置换子群

Let d be the smallest generator number of a finite p-group P and let Md（P） = {P1,...,Pd} be a set of maximal subgroups of P such that ∩di=1 Pi = Φ（P）. In this paper, we study the structure of a finite group G under the assumption that every member in Md（Gp） is S-semipermutable in G for each prime divisor p of ｜G｜ and a Sylow p-subgroup Gp of G.     

On SS-Quasinormal Subgroups of Finite Groups

A subgroup of a group G is said to be Sylow-quasinormal (S-quasinormal) in G if it permutes with every Sylow subgroup of G. A subgroup H of a group G is said to be Supplement-Sylow-quasinormal (SS-quasinormal) in G if there is a supplement B of H to G such that H is permutable with every Sylow subgroup of B. In this article, we investigate the influence of SS-quasinormal of maximal or minimal subgroups of Sylow subgroups of the generalized Fitting subgroup of a finite group.     

On Nearly SS-Embedded Subgroups of Finite Groups

Let H be a subgroup of a finite group G. H is nearly SS-embedded in G if there exists an S-quasinormal subgroup K of G, such that HK is S-quasinormal in G and H ∩ K ≤ HseG, where HseG is the subgroup of H, generated by all those subgroups of H which are S-quasinormally embedded in G. In this paper, the authors investigate the influence of nearly SS-embedded subgroups on the structure of finite groups.     

On Nearly S-Permutable Subgroups of Finite Groups

We say that a subgroup H of a finite group G is nearly S-permutable in G if for every prime p such that (p, |H|) = 1 and for every subgroup K of G containing H the normalizer N _K (H) contains some Sylow p-subgroup of K. We study the structure of G under the assumption that some subgroups of G are nearly S-permutable in G.     

On Solvable Normal Subgroups of Finite Groups

We consider solvable invariant subgroups of a finite group with bounded primary indices of maximal subgroups. We establish that an invariant subgroup of this type belongs to the product of classical formations and investigate its dispersibility.     

On Reflection Subgroups of Finite Coxeter Groups

Let W be a finite Coxeter group. We classify the reflection subgroups of W up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup R of W the conjugacy class of its Coxeter elements to be injective, up to conjugacy.     

On Primary Abelian Groups Modulo Finite Subgroups

We study the existence of several classes 𝒦 of Abelian p-groups, p a fixed prime, which possess the following property: A ∈ 𝒦?A/F ∈ 𝒦, whenever F is a finite subgroup of the Abelian p-group A.     

On Semi Cover-Avoiding Maximal Subgroups of Sylow Subgroups of Finite Groups

A subgroup H of a finite group G is called to have semi cover-avoiding property in G if there is a normal series of G such that H either covers or avoids every normal factor of the series. In this article we get some new results under the assumption that every maximal subgroup of Sylow subgroups of a suited subgroup of G has semi cover-avoiding property in G. We state our results in the broader context of formation theory.