Groups of Prime Power Order

Berkovich (retired, mathematics, U. of Haifa, Israel) continues his exposition of the theory of finite prime power order groups (p-groups), moving on to more complex materials and adding material on 2- groups in sections separately authored by Janko (emeritus, Institute of Mathematics, U. of Heidelberg, Germany). Topics covered in this volume includes classification of p-groups all of whose cyclic subgroups of composited orders are normal, classification of 2-groups with exactly three involutions, proofs of Ward's theorem on quaternion-free groups, 2-groups with small centralizers of an involution, classification of 2-groups with exactly four cyclic subgroups of order 2n greater than 2, proofs of Blacuburn's theorem on minimal nonmetacyclic groups, classification of p-groups all of whose subgroups of index p2 are abelian, classification of 2-groups all of whose minimial nonabelian subgroups have order 8, and classification of p-groups with cyclic subgroups of index p2. Original exercises with solutions are included, along with a list of some 700 open problems. Annotation c2009 Book News, Inc., Portland, OR (booknews.com)

Yakov Berkovich, University of Haifa, Israel; Zvonimir Janko, Universitat Heidelberg.