The maximal subgroups of Sylow subgroups and the structure of finite groups
نویسندگان
چکیده
منابع مشابه
ON 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 کاملThe 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 $G$.
متن کاملMaximal 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...
متن کاملPOS-groups with some cyclic Sylow subgroups
A finite group G is said to be a POS-group if for each x in G the cardinality of the set {y in G | o(y) = o(x)} is a divisor of the order of G. In this paper we study the structure of POS-groups with some cyclic Sylow subgroups.
متن کاملThe Sylow Subgroups of the Symmetric Groups
The aim of this paper is to give a direct approach to the study of the Sylow ^-subgroups Sn of the symmetric group of degree pn. [We assume throughout that p^2.] Many of the results are already known and are treated in a paper by Kaloujnine where he uses a particular representation by means of "reduced polynomials."1 It has seemed worth while to restate some of his results using the concept of ...
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ژورنال
عنوان ژورنال: Boletim da Sociedade Paranaense de Matemática
سال: 2017
ISSN: 2175-1188,0037-8712
DOI: 10.5269/bspm.v37i1.20200