The papers of the present volume represent the proceedings of the
Conference entitled "Ischia Group Theory 2004," which took place at the Jolly
Hotel, Ischia (Naples, Italy), from March, 31st to April, 3rd 2004, in honour of
MARCEL HERZOG. The organizing committee consisted of ZVI ARAD, MARIA-
GRAZIA BIANCHI, PATRIZIA LONGOBARDI, MERCEDE MAJ and CARLO SCOPPOLA.
The local committee was formed by COSTANTINO DELIZIA, CHIARA NICOTERA,
CARMELA SICA and MARIA TOTA, all from the Universita di Salerno. The articles
in this volume, most of which are close to areas of research of Marcel Herzog, are
contributions by speakers and participants of the conference.
The following topics are represented by the articles: combinatorial questions,
such as counting the number of conjugacy classes of a group, or investigating the
covering number of a simple group; the (sub)group structure of groups, such as
recognizing the structure of a p-group when there are restrictions on certain of its
subgroups; groups with a bound on the number of commutator in groups; classi-
fication of Hall subgroups of almost simple groups; classification of groups with a
CC-subgroup; algebras, mostly connected to or motivated from character theory;
table algebras; group rings with a simple augmentation ideal; probabilistic methods
(mainly for profinite groups); graphs with groups of automorphisms acting primi-
tively on vertices; certain graphs connected with groups, such as the commutativity
graph or the prime graph.
A poster session on various topics connected with themes of the conference
augmented the scientific program.
It is our pleasure to thank the organizers and particularly our colleagues from
the Universita di Salerno, who made our stay and work extremely pleasant; the
referees of the papers for spending many hours reviewing papers and providing
valuable feedback to the authors; the authors of all submitted papers for their con-
tributions; the staff of the JOLLY HOTEL for having been very accommodating and
supportive; the AMERICAN MATHEMATICAL SOCIETY and BAR-ILAN UNIVERSITY
for their kind support for producing these proceedings in a professional and timely
manner; MIRIAM BELLER for her expert assistance in compiling this volume; and,
of course, MARCEL HERZOG for allowing us to celebrate with him.