READING OFF KUROSH DECOMPOSITIONS

Reading 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...

Reading Off Kurosh Decompositions

Geometric methods proposed by Stallings [17] 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, 6, 10, 11, 15, 16, 20]. In the present paper we employ the generalized Stallings’ folding method developed in [12] to introduce a procedure, which given a subgroup H of a free product ...

On the Kurosh Theorem and Separability

Kurosh-amitsur Radical Theory for Groups

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.

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...