Leibniz n-超代数的Frattini-子代数

给出了Leibniz n-超代数的Frattini-子代数的一些重要性质,确定了Leibniz n-超代数的Frattini-子代数的分解定理,并且利用所得到的Frattini-子代数的重要性质,Leibniz n-超代数是幂零的一个必要条件被给出.     

The nilpotence class of the Frattini subgroup

Ap-group of sufficiently large nilpotence class cannot occur as a normal subgroup contained in the Frattini subgroup of any finite group. The Frattini subgroup of a group of order Π _pi ^αi with max α _i at least 3, has nilpotence class at most 1/2 (max α _i − 1). The Frattini subgroup of at-group is abelian. The occurrence of groups of orderp ⁴ as normal subgroups contained in Frattini subgroups is investigated. National Science Foundation Science Faculty Fellow, University of Cincinnati     

The Frattini Subalgebra of Restricted Lie Superalgebras

In the present paper, we study the Frattini subalgebra of a restricted Lie superalgebra （L, [p]）. We show first that if L = A1 ＋ A2 ＋… ＋An, then Фp（L） = Фp（A1） ＋Фp（A2） ＋…＋Фp（An）, where each Ai is a p-ideal of L. We then obtain two results： F（L） = Ф（L） = J（L） = L if and only if L is nilpotent; Fp（L） and F（L） are nilpotent ideals of L if L is solvable. In addition, necessary and sufficient conditions are found for Фp-free restricted Lie superalgebras. Finally, we discuss the relationships of E-p-restricted Lie superalgebras and E-restricted Lie superalgebras.     

李三系的Frattini子系

李三系是从黎曼对称空间产生的三元运算的代数系统,近年来备受数学家们的重视.针对李三系的Frattini子系和基本李三系的问题进行了研究,给出了Frattini子系和基本李三系的一些性质,并证明了李三系的非嵌入定理,同时得到了幂零李三系是基本李三系的一个充要条件.     

李超三系的Frattini-子系

In the present paper,we develop initially the Frattini theory for Lie supertriple systems,obtain some properties of the Frattini subsystem and show that the intersection of all maximal subsystems of a solvable Lie supertriple system is its ideal.Moreover,we give the relationship between φ-free and complemented for Lie supertriple system.     

The Frattini sublattice of a finite distributive lattice

Frattini sublattices of finite distributive lattices are characterized and several applications are given thereof.Presented by J. Berman.The support of Consejo Nacional de Investigaciones Cientificas y Técnicas de la República Argentina is gratefully acknowledged.     

Deciding Frattini is NP-complete

We show that it is a NP-complete problem to decide whether a finite poset arises as the (Birkhoff) dual of the Frattini sublattice of some finite distributive lattice.This work was supported in part by Swiss NSF grant 20-32644.91.     

Frattini subgroups and supernilpotent groups

In the context of the problem of which nonabelianp-groups can occur as normal subgroups contained in Frattini subgroups, the family of supernilpotent groups (all maximal subgroups characteristic) is investigated. Results of this investigation are applied to the Frattini-embedding problem, incorporating recent work of A. R. Makan. The groups of order 2ⁿ (n ≦ 6) have been examined with respect to supernilpotence and their occurrence as normal subgroups contained in Frattini subgroups. Results of this examination are presented.     

Two-generator Frattini subgroups of finitep-groups

This paper deals with nonabelianp-groupsT (p a prime andp>2) which are either metacyclic or Redei. These groups are classified into those which are Frattini subgroups of a finitep-groupG and those which are not. Finally, it is shown that a nonabelian two-generator group of orderp ⁿ (n>4) which is the Frattini subgroup of ap-group must be metacyclic. This work is contained in the author’s dissertation.     

Frattini subgroups ofp-closed andp-supersolvable groups

A nonabelianp-group with cyclic center cannot occur as a normal subgroup contained in the Frattini subgroup of ap-closed group. If a nonabelian normal subgroup of orderp ⁿ and nilpotence classk is contained in the Frattini subgroup of ap-closed group, then its exponent is a divisor ofp ^n−k . This fact is used to derive a relation among the order, number of generators, exponent, and class of the Frattini subgroup, forp-groups. Finally, it is conjectured that a nonabelianp-group having center of orderp cannot occur as a normal subgroup contained in the Frattini subgroup of any finite group. A proof is given forp-supersolvable groups.