Algebraic groups and lie groups with few factors / Alfonso Di Bartolo, Giovanni Falcone, Peter Plaumann... [et al.]

The authors study both algebraic groups and real and complex Lie groups by imposing on their connected subgroups the analogues of familiar conditions in abstract group theory. In particular, chains of connected subgroups play a central role. An algebraic group whose connected subgroup lattice is a chain is called a chain. A class of examples are the commutative Witt groups. Also, the abstract concept of normal subgroup and generalizations find suitable concepts in the present study. In particular Hamiltonian algebraic groups are defined and investigated.

A theme the authors provide is the difference between algebraic groups of characteristic zero and p. They study maximal nilpotency class, the analogue of current topics of interest in p-groups and Lie algebras. There is a long chapter on the topic of isogeneous factors.

This book serves as a valuable resource to those working in the field of algebraic groups and as a good place to learn about this aspect of that field. (Zentralblatt)