5.3 GROUP THEORY – II
UNIT-I
Automorphisms, The Centre of a group, Automorphisms of a cyclic group, Conjugacy,
G-sets.
UNIT-II
Normal series, Jordan-Holder Theorem, Solvable groups, Nilpotent groups.
UNIT-III
Permutation groups, Cyclic Decomposition, Alternating Group An, Simple groups, Simplicity of A¬n.
UNIT-IV
Structure Theorems of groups, Direct products, Fundamental Theorem of finitely generated Abelion groups, Invariants of a finite Abelion group, Singlow Theorems, Cauchy theorem, Groups of order p2 and pq.
Text book:
Basic Abstract algebra by P.B.Bhattacharya, S.K.Jain and S.R.Nagpaul, Cambridge University Press, 1995.
References:
[1] Algebra by Michael Artin, Prentice Hall of India Private Limited, New Delhi, 1996.
[2] Topics in Algebra by I.N.Herstien, Second Edition, John Wiley & Sons, NewYork, 1975.
[3] Algebra by Serge Lang, Third Edition, Pearson Education, 2001.
[4] A First Course in Abstract Algebra by J.B.Fraileigh, Fifth Edition, Addison-Wesley, 1999.
Reference http://www.nannayauniversity.info/courses.html
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