Kurosh-amitsur Radical Theory for Groups
نویسنده
چکیده
This is a survey of some aspects of Kurosh-Amitsur radical theory for groups which touches on history, some links and contrasts with ring radicals and some recent appearances of group radicals in the mathematical literature.
منابع مشابه
On Kurosh-amitsur Radicals of Finite Groups
Between 1952 and 1954 Amitsur and Kurosh initiated the general theory of radicals in various contexts. In the case of all groups some interesting results concerning radicals were obtained by Kurosh, Shchukin, Ryabukhin, Gardner and others. In this paper we are going to examine radical theory in the class of all finite groups. This strong restriction gives chance to obtain stronger results, then...
متن کاملNon-pointed Exactness, Radicals, Closure Operators
In this paper it is shown how non-pointed exactness provides a framework which allows a simple categorical treatment of the basics of KuroshAmitsur radical theory in the non-pointed case. This is made possible by a new approach to semi-exactness, in the sense of the first author, using adjoint functors. This framework also reveals how categorical closure operators arise as radical theories.
متن کاملKurosh-Amitsur Right Jacobson Radical of Type 0 for Right Near-Rings
By a near-ring we mean a right near-ring. J 0 , the right Jacobson radical of type 0, was introduced for near-rings by the first and second authors. In this paper properties of the radical J 0 are studied. It is shown that J 0 is a Kurosh-Amitsur radical KA-radical in the variety of all near-rings R, in which the constant part Rc of R is an ideal of R. So unlike the left Jacobson radicals of ty...
متن کاملHereditary right Jacobson radicals of type-1(e) and 2(e) for right near-rings
Near-rings considered are right near-rings. In this paper two more radicals, the right Jacobson radicals of type-1(e) and 2(e), are introduced for near-rings. It is shown that they are Kurosh-Amitsur radicals (KAradicals) in the class of all near-rings and are ideal-hereditary radicals in the class of all zero-symmetric near-rings. Different kinds of examples are also presented.
متن کاملReading off Kurosh Decompositions
Geometric methods proposed by Stallings [13] for treating finitely generated subgroups of free groups were successfully used to solve a wide collection of decision problems for free groups and their subgroups [1, 5, 9, 10, 16]. In the present paper we employ the generalized Stallings’ folding method developed in [11] to introduce a procedure, which given a subgroup H of a free product of finite...
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تاریخ انتشار 2010