The impetus for current research in pro-p groups comes from four main directions: from new applications in number theory, which continue to be a source of deep and challenging problems; from the traditional problem of classifying finite p-groups; from questions arising in infinite group theory; and finally, from the younger subject of 'profinite group theory'. A correspondingly diverse range of mathematical techniques is being successfully applied, leading to new results and pointing to exciting new directions of research.
In this work important theoretical developments are carefully presented by leading mathematicians in the field, bringing the reader to the cutting edge of current research. With a systematic emphasis on the construction and examination of many classes of examples, the book presents a clear picture of the rich universe of pro-p groups, in its unity and diversity. Thirty open problems are discussed in the appendix.
For graduate students and researchers in group theory, number theory, and algebra, this work will be an indispensable reference text and a rich source of promising avenues for further exploration.
Lie methods in the theory of pro-p groups, A. Shalev; on the classification of prop-p groups and finite p-groups, C.R. Leedham-Green, S. McKay; prop-p trees and applications, L. Ribes, P. Zalesskii; just infinite branch groups, R. I. Grigorchuk; on just infinite abstract and profinite groups, J.S. Wilson; the Nottingham group, R. Camina; on groups satisfying the Golod-Shafarevich condition, E. Zelmanov; sub-group growth in prop-p groups, A. Mann; zeta functions of groups, M. du Sautoy, D. Segal; where the wild things are - ramification groups and the Nottingham group, M. du Sautoy, I. Fesenko; p-adic Galois representations and prop-p Galois groups, N. Boston; the cohomology of p-adic analytic groups, P. Symonds, T. Weigel. Appendix: further problems.
Series: Progress In Mathematics (BIRKHAUSER BOSTON)
Tertiary; University or College
Number Of Pages: 426
Published: 25th May 2000
Publisher: BIRKHAUSER BOSTON INC
Country of Publication: US
Dimensions (cm): 23.5 x 15.24
Weight (kg): 0.77