Overview
- Elucidates automorphisms of groups as a fundamental topic of study in group theory
- Explores various developments on the relationship between orders of finite groups and their automorphism groups
- Provides a unified account of important group-theoretic advances arising from this study
- Includes open problems for future work
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (6 chapters)
Keywords
About this book
The book describes developments on some well-known problems regarding the relationship between orders of finite groups and that of their automorphism groups. It is broadly divided into three parts: the first part offers an exposition of the fundamental exact sequence of Wells that relates automorphisms, derivations and cohomology of groups, along with some interesting applications of the sequence. The second part offers an account of important developments on a conjecture that a finite group has at least a prescribed number of automorphisms if the order of the group is sufficiently large. A non-abelian group of prime-power order is said to have divisibility property if its order divides that of its automorphism group. The final part of the book discusses the literature on divisibility property of groups culminating in the existence of groups without this property. Unifying various ideas developed over the years, this largely self-contained book includes results that are either proved or with complete references provided. It is aimed at researchers working in group theory, in particular, graduate students in algebra.
Reviews
“The audience for this interesting book includes group theorists and graduate students headed in this direction.” (Michael Berg, MAA Reviews, October 6, 2019)
“It represents a useful reference text for researchers in the area, but easily doubles as a very readable introductory text for graduate students … .” (Andrea Caranti, Mathematical Reviews, August, 2019)
Authors and Affiliations
About the authors
Mahender Singh is Assistant Professor at the Indian Institute of Science Education and Research, Mohali. He earned his Ph.D. in mathematics from Harish-Chandra Research Institute, Allahabad (2010). His research interests lie broadly in topology and algebra, with a focus on compact group actions on manifolds, equivariant maps, automorphisms and cohomology of groups, and quandles. He is a recipient of the INSPIRE Faculty award of the Department of Science and Technology, Government of India (2011). He has published several research papers in respected international journals, conference proceedings, and contributed volumes.
Manoj Kumar Yadav is Professor at the Harish-Chandra Research Institute, Allahabad. He received his Ph.D. in mathematics from Kurukshetra University, Haryana (2002). He is a recipient of the Indian National Science Academy Medal for Young Scientists (2009) and the Department of Science and Technology, Science and Engineering Research Council (SERC), fellowship Fast Track Scheme for Young Scientists (2005). He is a member of the National Academy of Sciences, India (NASI). His research interests lie in group theory, particularly the automorphisms, conjugacy classes, and Schur multipliers of groups. He has published several research papers in respected international journals, conference proceedings, and contributed volumes.
Bibliographic Information
Book Title: Automorphisms of Finite Groups
Authors: Inder Bir Singh Passi, Mahender Singh, Manoj Kumar Yadav
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-981-13-2895-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer Nature Singapore Pte Ltd. 2018
Hardcover ISBN: 978-981-13-2894-7Published: 22 January 2019
eBook ISBN: 978-981-13-2895-4Published: 12 January 2019
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: XIX, 217
Number of Illustrations: 1 b/w illustrations
Topics: Group Theory and Generalizations, Topological Groups, Lie Groups, Several Complex Variables and Analytic Spaces, Number Theory