Maximal subgroups of finite groups avoiding the elements of a generating set

Maximal Subgroups of Finite Groups

What ingredients are necessary to describe all maximal subgroups of the general finite group G? This paper is concerned with providing such an analysis. A good first reduction is to take into account the first isomorphism theorem, which tells us that the maximal subgroups containing a given normal subgroup N of G correspond, under the natural projection, to the maximal subgroups of the quotient...

The nc-supplemented subgroups of finite groups

A subgroup $H$ is said to be $nc$-supplemented in a group $G$ if there exists a subgroup $Kleq G$ such that $HKlhd G$ and $Hcap K$ is contained in $H_{G}$, the core of $H$ in $G$. We characterize the supersolubility of finite groups $G$ with that every maximal subgroup of the Sylow subgroups is $nc$-supplemented in $G$.

Finite Groups With a Certain Number of Elements Pairwise Generating a Non-Nilpotent Subgroup

Computing maximal subgroups of finite groups

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.

On Maximal Subgroups of Finite Classical Groups

In 1] M. Aschbacher described the structure of the possible maximal subgroups of a classical group G with natural module M. Each such subgroup is either a member of a canonical class of subgroups, or it is the normalizer of a quasi-simple, absolutely irreducible subgroup H of G. In the latter case suppose that H is a classical group whose deening characteristic is coprime to that of G. The aim ...