In the present paper,we investigate solvable radicals and Hopkins nilpotent radicals for Lie triple systems and prove that both radicals are invariant under actions of deriva- tions.
本文讨论李三系的可解根基和Hopking幂零的某些性质及导子作用下的不变性,讨论了李三系次理想的某些性质,证明了李三系为幂零的当且仅当每个子系都是次理想。
After giving the concept and some elementary properties of subideals of Lie triple system,the author shows that every subalgebra of a nilpotent Lie triple systems is a subideal and a Lie triple system is solvable if every subalgebra is a subideal.
证明了幂零李三系的子系数都是次理想;当李三系的所有子系数都是次理想时,该李三系是可解的。
This paper discusses the influence of the θ-pairs associted to a famity of special maximal subgroups of a group on the group and establishes some necessary and sufficient conditions for a group to be solvable.
讨论有限群的一类特殊极大子群的θ-子群偶对该群可解性的影响,得到若干充要条件,推广了该方面已有的一些结论。
In this paper,we research the effect of c-normality on supersolvablity and solvability,and get some good results:if M is a normal subgroup of G and every sylow subgroup of M is c-niomal in G, then G is supersolvable;let M be normal and maximal in G, if every subgroup of prime order is c-normal in G,and every Frattini subgroup of sylow subgroups in G is 1.
我们运用C-正规性质来刻画群的可解性和超可解性,并得到了一些很好的结论:设M为群G的一个极大子群,若M的任一Sylow子群在G中C-正规,则G超可解;MG,且为G之极大子群,M的每一个素数阶子群在G中C-正规及M的任何Sylow子群的Frattini子群为1,则G超可解。
We get some results about the solvability of G.
一个群G的子群H被称为CAP-子群,若它满足H或是覆盖或是避开G的每一个主因子,群G的子群H被称为半CAP-子群,若它满足H或是覆盖或是避开G的某个固定主群列的每一个主因子,本文通过假定群G的某些子群为CAP-子群或半CAP-子群,给出了群的可解性的某些刻画。
The solvability and nilpotency of Novikov algebras are discussed.
讨论了Novikov代数的幂零性和可解性,得到了可解理想之和可解,可解Novikov代数的子代数和同态象可解等结论,以及与之相联系的李代数的可解幂零性的关系。