In theory there is no difference between theory and practice. In practice there is. Yogi Berra
A SINGULAR Introduction to Commutative Algebra offers a rigorous intro duction to …

A comprehensive study of the main research done in polynomial identities over the last 25
years, including Kemer's solution to the Specht problem in characteristic O and examples in …

We prove that the solvable radical of a finite group G coincides with the set of elements y
having the following property: for any x∈ G the subgroup of G generated by x and y is …

We present a survey of results on word equations in simple groups, as well as their
analogues and generalizations, which were obtained over the past decade using various …

This edition presents the underlying ideas in recent polynomial identity (PI)-theory and
demonstrates the validity of the proofs of PI-theorems. It gives all the details involved in …

We obtain the following characterization of the solvable radical R (G) of any finite group G: R
(G) coincides with the collection of all g∈ G such that for any 3 elements a1, a2, a3∈ G the …

We characterise the class of finite solvable groups by two-variable identities in a way similar
to the characterisation of finite nilpotent groups by Engel identities. Let holds in G. We also …

We study dynamical systems arising from word maps on simple groups. We develop a
geometric method based on the classical trace map for investigating periodic points of such …

Engel groups and Engel elements became popular in 50s. We consider in the paper the
more general nil-groups and nil-elements in groups. All these notions are related to nilpotent …

We give a survey of new characterizations of finite solvable groups and the solvable radical
of an arbitrary finite group which were obtained over the past decade. We also discuss …