c-Sections of Maximal Subgroups of Finite Groups
نویسندگان
چکیده
منابع مشابه
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...
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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.
متن کاملOn 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 ...
متن کاملON c-SUPPLEMENTED MAXIMAL AND MINIMAL SUBGROUPS OF SYLOW SUBGROUPS OF FINITE GROUPS
This paper proves: Let F be a saturated formation containing U . Suppose that G is a group with a normal subgroup H such that G/H ∈ F . (1) If all maximal subgroups of any Sylow subgroup of F ∗(H) are c-supplemented in G, then G ∈ F ; (2) If all minimal subgroups and all cyclic subgroups with order 4 of F ∗(H) are c-supplemented in G, then G ∈ F .
متن کاملmaximal Subgroups in Composite Finite Groups
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 ...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2000
ISSN: 0021-8693
DOI: 10.1006/jabr.2000.8268