Automorphisms of Finite Groups (eBook)

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; Professor at Panjab University, Chandigarh; Visiting Professor at the University of California, Los Angeles; Universitaet Goettingen, Goettingen; 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 ten books including Group Rings and Their Augmentation Ideals and Lower Central and Dimension Series of Groups (both with Springer), as well as several 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 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.

Introduction.- p-groups.- Fundamental exact sequence of Wells.- Automorphism groups of finite groups.- Groups with Divisibility Property-I.- Groups with Divisibility Property-II.- Groups without Divisibility Property.