On recognition of the projective special linear groups over binary fields.
On regular automorphisms of order 3 and Frobenius pairs.
On Rough Subgroup of a Group
This article describes a rough subgroup with respect to a normal subgroup of a group, and some properties of the lower and the upper approximations in a group.
On -quasinormal and -normal subgroups of a finite group
Let be a saturated formation containing the class of supersolvable groups and let be a finite group. The following theorems are presented: (1) if and only if there is a normal subgroup such that and every maximal subgroup of all Sylow subgroups of is either -normal or -quasinormally embedded in . (2) if and only if there is a normal subgroup such that and every maximal subgroup of all Sylow subgroups of , the generalized Fitting subgroup of , is either -normal or -quasinormally...
On self-centralizing Sylow subgroups of order four
On small distances of small 2-groups
The paper reports the results of a search for pairs of groups of order that can be placed in the distance for the case when . The constructions that are used are of the general character and some of their properties are discussed as well.
On sM-group.
On soluble groups of automorphisms of nonorientable Klein surfaces
We classify up to topological type nonorientable bordered Klein surfaces with maximal symmetry and soluble automorphism group provided its solubility degree does not exceed 4. Using this classification we show that a soluble group of automorphisms of a nonorientable Riemann surface of algebraic genus q ≥ 2 has at most 24(q-1) elements and that this bound is sharp for infinitely many values of q.
On solvability of finite groups with some -supplemented subgroups
A subgroup of a finite group is said to be -supplemented in if there exists a subgroup of such that and is -permutable in . In this paper, we first give an example to show that the conjecture in A. A. Heliel’s paper (2014) has negative solutions. Next, we prove that a finite group is solvable if every subgroup of odd prime order of is -supplemented in , and that is solvable if and only if every Sylow subgroup of odd order of is -supplemented in . These results improve...
On Solvable Groups with a Minimal Normal P-Subgroup
On some finite 2-groups in which the derived group has two generators
We show that any finite 2-group, whose abelianization has either 4-rank at most 2 or 8-rank 0 and whose commutator subgroup is generated by two elements, is metabelian. We also prove that the minimal order of any 2-group with nonabelian commutator subgroup of 2-rank 2 is .
On Some Finite 2-Groups of Deficiency Zero
On some maximal -quasinormal subgroups of finite groups.
On some metabelian 2-groups and applications I
Let G be some metabelian 2-group satisfying the condition G/G’ ≃ ℤ/2ℤ × ℤ/2ℤ × ℤ/2ℤ. In this paper, we construct all the subgroups of G of index 2 or 4, we give the abelianization types of these subgroups and we compute the kernel of the transfer map. Then we apply these results to study the capitulation problem for the 2-ideal classes of some fields k satisfying the condition , where is the second Hilbert 2-class field of k.
On some permutable products of supersoluble groups.
It is well known that a group G = AB which is the product of two supersoluble subgroups A and B is not supersoluble in general. Under suitable permutability conditions on A and B, we show that for any minimal normal subgroup N both AN and BN are supersoluble. We then exploit this to establish some sufficient conditions for G to be supersoluble.
On special -groups
In questo lavoro viene data una caratterizzazione di quei -gruppi nilpotenti di classe due ed esponente che sono speciali. Vengono inoltre studiate alcune costruzioni, automorfismi e sottogruppi abeliani di -gruppi speciali.
On S-quasinormal subgroups of finite group.
On strong reality of the unipotent Lie-type subgroups over a field of characteristic 2.
On subgroups of ZJ type of an F-injector for Fitting classes F between Ep*p and Ep*Sp.
Let G be a finite group and p a prime. We consider an F-injector K of G, being F a Fitting class between Ep*p y Ep*Sp, and we study the structure and normality in G of the subgroups ZJ(K) and ZJ*(K), provided that G verifies certain conditions, extending some results of G. Glauberman (A characteristic subgroup of a p-stable group, Canad. J. Math.20(1968), 555-564).
On supersoluble groups acting on Klein surfaces.