Abstract A Grigorchuk–Gupta–Sidki (GGS)-group is a subgroup of the automorphism group p -regular rooted tree for an odd prime , generated by one and directed automorphism. Pervova proved that all torsion GGS-groups do not have maximal subgroups infinite index. Here, we extend result to nontorsion GGS-groups, which include weakly regular branch, but GGS-group.

In this paper we show how to construct the maximal subgroups of the finite classical groups of linear, symplectic or unitary type in low-degree

We describe a practical algorithm for computing representatives of the conjugacy classes of maximal subgroups in a finite group, together with details of its implementation for permutation groups in the MAGMA system. We also describe methods for computing complements of normal subgroups and minimal supplements of normal soluble subgroups of finite groups.

Definition 1. Let G be a permutation group on a set  and x be an element of . Then Gx  g ∈ G ∣ gx  x is called the stabilizer of x and consists of all the permutations of G that produce group fixed points in x. Definition 2. A vector subspace S ⊂ V is isotropic if for any v,w ∈ S, the symmetric bilinear form satisfies: Bv,w  0 Definition 3. A maximal parabolic subgroup in an orthogon...

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 ...