For a finite group G, subgroup P of G is 2-minimal if B<P, where B=NG(S) for some Sylow 2-subgroup S and B contained in unique maximal P. fields odd characteristic, this paper contains detailed explicit description all the subgroups general orthogonal groups, certain their subgroups.

The purpose of this paper is to present a method for translating the problem of finding all maximal subgroups of finite groups into questions concerning groups that are nearly simple. (A finite group is called nearly simple if it has only one minimal normal subgroup and that it nonabelian and simple.) In view of the recently announced classification of all finite simple groups this seems to be ...

‎In the classical group theory there is‎ an open question‎: ‎Is every torsion free n-Engel group (for n ≥ 4)‎, nilpotent?‎. ‎To answer the question‎, ‎Traustason‎ [11] showed that with some additional conditions all‎ ‎4-Engel groups are locally nilpotent‎. ‎Here‎, ‎we gave some partial‎ answer to this question on Engel fuzzy subgroups‎. ‎We show that if μ is a normal 4-Engel fuzzy‎ subgroup of ...

We study the minimal normal completion problem: given A ∈ Cn×n, how do we find an (n+q)×(n+q) normal matrix Aext := ( A A12 A21 A22 ) of smallest possible size? We will show that this smallest number q of rows and columns we need to add, called the normal defect of A, satisfies nd(A) ≥ max{i−(AA∗ −A∗A), i+(AA∗ −A∗A)}, where i±(M) denotes the number of positive and negative eigenvalues of the He...

The concept of critical group was introduced by D. C. Cross (as reported by G. Higman in [5]): a finite group is called critical if it is not contained in the variety generated by its proper factors. (The factors of a group G are the groups HjK where K < H gj G, and H]K is a proper factor of G unless H = G and K = 1 ) . Some investigations concerning finite groups and varieties depend on the in...