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...

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...

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.

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 ...

The Relationship Between Concussion History and Post-Concussion Neuropsychological Performance and Symptoms in Collegiate Athletes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Tracey Covassin, David Stearne Gender Differences on Neuromuscular Control of the Hip: Implications for Knee Joint Stability and Non-Contact Anterior Cr...

We consider a couple of versions of classical Kurosh problem (whether there is an infinite-dimensional algebraic algebra?) for varieties of linear multioperator algebras over a field. We show that, given an arbitrary signature, there is a variety of algebras of this signature such that the free algebra of the variety contains multilinear elements of arbitrary large degree, while the clone of ev...

Let G = ∗ i=1 Gi and let φ be a symmetric endomorphism of G. If φ is a monomorphism or if G is a finitely generated residually finite group, then the fixed subgroup Fix(φ) = {g ∈ G : φ(g) = g} of φ has Kurosh rank at most n.

We provide elementary proofs of the Nielsen-Schreier Theorem and the Kurosh Subgroup Theorem via wreath products. Our proofs are diagrammatic in nature and work simultaneously in the abstract and profinite categories. A new proof that open subgroups of quasifree profinite groups are quasifree is also given.