Springer Monographs in Mathematics

Automorphisms of Finite Groups

Authors: Passi, Inder Bir Singh, Singh, Mahender, Yadav, Manoj Kumar

  • 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
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eBook $84.99
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  • Due: January 17, 2019
  • ISBN 978-981-13-2895-4
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover $109.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: December 20, 2018
  • ISBN 978-981-13-2894-7
  • Free shipping for individuals worldwide
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.

About the authors

INDER BIR SINGH PASSI is Professor Emeritus at Panjab University, Chandigarh; Honorary Professor at the Indian Institute of Science Education and Research, Mohali; Professor at Ashoka University, Sonipat; and INSA Emeritus Scientist. Earlier, he has held several academic positions including Professor at Kurukshetra University, Kurukshetra (Haryana); Professor at Panjab University, Chandigarh; Visiting Professor at the University of California, Los Angeles (USA), Universitaet Goettingen, Goettingen (Germany), and Harish-Chandra Research Institute, Allahabad. He is a recipient of the Shanti Swarup Bhatnagar Prize for Mathematical Sciences (1983), the Meghnad Saha Award for Research in Theoretical Sciences (1988), the Distinguished Service Award (2003) by Mathematical Association of India; Khosla National Award (2011) by the Indian Institute of Technology Roorkee; and Prasanta Chandra Mahalanobis Medal (2011) by the Indian National Science Academy. His research interests are in algebra, particularly in group theory and group rings. He has published/co-authored/edited more than 10 books including Group Rings and Their Augmentation Ideals and Lower Central and Dimension Series of Groups (both with Springer), as well as numerous research papers in respected international journals, conference proceedings and contributed volumes. MAHENDER SINGH is Assistant Professor at the Indian Institute of Science Education and Research, Mohali. He earned his PhD 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 over 25 research papers in various respected journals, conference proceedings and contributed volumes. MANOJ KUMAR YADAV is Professor of Mathematics at the Harish-Chandra Research Institute, Allahabad. He received his PhD in Mathematics from Kurukshetra University, Haryana (2002). He has been awarded the Indian National Science Academy Medal for Young Scientists (2009) and the Department of Science & 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 (NASI), India. His research interests lie in group theory, particularly the automorphisms, conjugacy classes and Schur multipliers of groups. He has published over 25 research papers in various respected journals, conference proceedings and contributed volumes.

Buy this book

eBook $84.99
price for USA in USD (gross)
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: January 17, 2019
  • ISBN 978-981-13-2895-4
  • Digitally watermarked, DRM-free
  • Included format:
  • ebooks can be used on all reading devices
Hardcover $109.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: December 20, 2018
  • ISBN 978-981-13-2894-7
  • Free shipping for individuals worldwide
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Bibliographic Information

Bibliographic Information
Book Title
Automorphisms of Finite Groups
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2018
Publisher
Springer Singapore
Copyright Holder
Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-13-2895-4
DOI
10.1007/978-981-13-2895-4
Hardcover ISBN
978-981-13-2894-7
Series ISSN
1439-7382
Edition Number
1
Number of Pages
X, 208
Topics